The 82-year-old actress recalled on the CBS late-night program how Stewart, her idol, surprised her by showing up to the finale of The Carol Burnett Show in 1978. Decades later, Colbert had a similar surprise up his sleeve.
The sweet, silly poem brought tears to Burnett's eyes. "The drinks are on me all night at the bar," Spacey, as Stewart, recited as Burnett became emotional, "because Carol Burnett is still comedy's greatest star."
Photos of Carol Burnett from over the years:
Kevin Spacey brings Carol Burnett to tears with Jimmy Stewart impression
Carol Burnett, 24, sings her rendition of "I Made a Fool of Myself Over John Foster Dulles" on Aug. 14, 1957. (AP Photo)
Two "cowboys," Carol Burnett, left, and Julie Andrews, rehearse in New York's Carnegie Hall for a one-time TV show, "Julie and Carol at Carnegie Hall," March 8, 1962. (AP Photo/Bob Wands)
Comedian Carol Burnett is shown Feb. 7, 1963. She will be featured in her own CBS special, "Carol and Company." (AP Photo)
Comedian Garry Moore kisses Carol Burnett at the Hotel Astor in New York, May 22, 1962, after they received Emmy Awards for "The Garry Moore Show." (AP Photo/Eddie Adams)
Comedian, actress, singer and dancer Carol Burnett is shown in 1967. (AP Photo)
Comedian Carol Burnett is seen imitating Shirley Temple in "Fade Out, Fade In," a musical on Broadway, July 10, 1964. (AP Photo)
Comedian Carol Burnett and Jan-Michael Vincent are seen at the Golden Globe awards in Hollywood, Calif., Jan. 19, 1977. (AP Photo)
FILE - In this March 19, 1978 black-and-white file photo, Carol Burnett shares a laugh with Tim Conway during taping of her final show , in Los Angeles. Burnett, who honed her humor on Broadway and landed her own comedy show on television in 1967, will win the nationâs top humor prize. The Kennedy Center for the Performing Arts announced Tuesday that Burnett will receive the Mark Twain Prize for American Humor on Oct. 20 in Washington. A gala performance featuring top names in comedy will be taped and broadcast nationally Oct. 30 on PBS. (AP Photo/ George Brich, File)
Comedian Carol Burnett and actor Alan Arkin are shown during the filming of a special Carol Burnett show in Los Angeles, Aug. 10, 1979, for the fall season. (AP Photo/George Brich)
Alan Alda looking happy with Carol Burnett as they hold their People?s Choic Awards, March 6, 1981 in Los Angeles. They were named the public?s favorite all-around best entertainer and favorite television performers in the male and female categories. (AP Photo)
LOS ANGELES, CA - FEBRUARY 21,1982: Actresses Carol Burnett and Lucille Ball onstage at the taping of the Bob Hope Special "The Women I Love: Beautiful, But Funny" on February 21, 1982 in Los Angeles, California. (Photo by TVA/PictureGroup/Invision for the Academy of Television Arts & Sciences/AP Images)
Comedian Carol Burnett and actor John Travolta are shown at the 55th Academy Awards where they were both presenters, April 11, 1983, in Hollywood. (AP Photo/Reed Saxon)
At Beverly Hills Hotel in Hollywood, Aug. 23, 1983, comedian Carol Burnett discusses the recent surgery she had on her jaw. The operation had a wonderful side-benefit, eliminating what she calls "the Burnett lower lip". (Ap Photo/Wally Fong)
A broadly-smiling Carol Burnett puts her hands to her cheeks inside a Los Angeles courtroom on Thursday, March 26, 1981 shortly after an 11-member jury ruled that the National Enquirer libeled Burnett in a 1976 gossip column. The jury ordered the tabloid to pay Burnett $1.6 million in damages. (AP Photo)
Carol Burnett, shown Nov. 17, 1987, simply wanted to do something funny on television and concluded that you canât get funnier than Neil Simon. She plays three different roles in a television adaption of Simonâs âPlaza Suiteâ that will be telecast on ABC-TV Thursday night. (AP Photo/Douglas C. Pizac)
Carol Burnett gives a kiss to Tony Bennett after he won an Emmy for outstanding performance for a variety or music program at the 48th Annual Primetime Emmy Awards in Pasadena, Calif., Sunday Sept. 8, 1996. He won for his performance "Tony Bennett Live by Request: A Valentine Special." (AP Photo/Mark J. Terrill)
Famed television performers Carroll O'Connor, left, and Carol Burnett pose together Monday, Nov. 11, 1996, during a private party at the House of Blues in West Hollywood, Calif., to celebrate the first 100 episodes of the NBC television comedy "Mad About You." O'Connor and Burnett make guest appearances in Tuesday night's episode of "Mad About You," playing the parents of Jamie, Helen Hunt's character on the show. (AP Photo/Chris Pizzello)
Actress and comedienne Carol Burnett poses next to a smiling caricature of herself as a ticket seller on a mural at a backstage VIP entrance to the newly-refurbished Pantages Theatre during rededication ceremonies Thursday, Sept. 28, 2000, in Los Angeles' Hollywood district. The Nederlander Organization Inc., which owns the theater, has spent nearly $10 million to restore it to the glitz and luster it had when first opening its doors in 1930. (AP Photo/Reed Saxon)
Legendary singer/actress Dame Julie Andrews, right, is joined by actress Carol Burnett during a reception honoring Andrews with the annual ELLA award in Beverly Hills, Calif., Wednesday, April 25, 2001. The award is given to singers whose contribution to the music world is equaled by a singer's humanitarian causes and community support. (AP Photo/Kevork Djansezian)
President Bush presents the Presidential Medal of Freedom to comediene Carol Burnett, left, on Wednesday, Nov. 9, 2005 in Washington. The Presidential Medal of Freedom is the nation's highest civilian award, and recognizes exceptional meritorious service. (AP Photo/Evan Vucci)
FILE - In this March 12, 2008 file photo, actress and comedienne Carol Burnett performs her famous Tarzan yell during her appearance on the NBC "Today" television program in New York. Burnett, who honed her humor on Broadway and landed her own comedy show on television in 1967, will win the nationâs top humor prize. The Kennedy Center for the Performing Arts announced Tuesday that Burnett will receive the Mark Twain Prize for American Humor on Oct. 20 in Washington. A gala performance featuring top names in comedy will be taped and broadcast nationally Oct. 30 on PBS. (AP Photo/Richard Drew, File)
Entertainer Carol Burnett describes the uniform she wore at a Southern California movie theater were she was fired when she was young, after her induction into the California Hall of Fame during ceremonies held at the California Museum in Sacramento, Calif., Tuesday, Dec. 1, 2009. Burnett was among 13 Californians inducted in to the hall of fame this year.(AP Photo/Rich Pedroncelli)
COMMERCIAL IMAGE - In this image provided by Geffen Playhouse, Dick Van Dyke and Carol Burnett attend the "Backstage At The Geffen" Fundraiser on Monday, June 4, 2012 in Los Angeles. (Photo by Jordan Strauss/Invision for Geffen Playhouse)
Carol Burnette arrives at the Academy of Television Arts and Sciences' An Evening with Carol Burnett at the Leonard H. Goldenson Theatre on Monday, July 22, 2013 in Los Angeles. (Photo by Richard Shotwell/Invision/AP)
Carol Burnett, right, is greeted by local photographer Anthony Frazier as she arrives at the Chestnut Ridge Resort in Blairsville, Pa. for a banquet to receive the 2014 Harvey Award presented by the Jimmy Stewart Museum on Friday, Oct. 3, 2014. (AP Photo/Keith Srakocic)
Actress Reese Witherspoon, left, watches entertainer Carol Burnett perform her Tarzan shout at the Wal-Mart shareholder meeting in Fayetteville, Ark., Friday, June 5, 2015. (AP Photo/Danny Johnston)
Spacey had another great moment during his appearance on TheLate Show. He revealed to Colbert just who he imagines he's talking to when his House of Cards character, Frank Underwood, turns to the camera.
"Who is that person? Is it like a close confidant," Colbert asked. "Because, the person you're actually talking to, of course, are the people on a 10-hour Netflix binge sucking on box wine."