The pair performed McCartney's song Queenie Eye to the star-studded crowd at the Staples Centre in Los Angeles.
Afterwards, Sir Paul and Starr held hands as they bowed and embraced as they received a standing ovation.
McCartney also won the Grammy for best long-form music video for Live Kisses during the event.
Earlier in the night Starr performed his solo offering Photograph and actress Julia Roberts announced the band will receive the 2014 Recording Academy Lifetime Achievement Award next month.
Daft Punk were the big prize winners of the night taking home album of the year for Random Access Memories and their collaboration with Pharrell Williams and Nile Rodgers, Get Lucky, won gongs for record of the year and best pop duo/group performance.
Meanwhile Adele added to her Grammy Awards haul by picking up a Best Song honour for her Skyfall James Bond theme.
American rap duo Macklemore and Ryan Lewis also won big as they took home gongs for best new artist, best rap performance and best rap song for Thrift Shop and best rap album for The Heist.
Jay Z, real name Shawn Carter, took home two awards for his collaborations with Justin Timberlake. He won best music video for Suit & Tie and best rap/sung collaboration for Holy Grail.
Timberlake also won best R&B song for Pusher Love Girl.
Royals by 17-year-old New Zealander Lorde won song of the year and best pop solo performance while Bruno Mars won best pop vocal album.
The ceremony was filled with huge performances throughout the night, with 33 couples getting married live on stage as Macklemore and Ryan Lewis performed their marriage equality anthem Same Love with guest appearances from Madonna and Mary Lambert.
The couples exchanged rings in the aisles of the Staples Centre as singer Queen Latifah performed the ceremony.
Standing next to Madonna, who was dressed all in white with a white cowboy hat, the Chicago star said: "By the power vested in me by the state of California, I now pronounce you married."
Speaking to the press after the awards ceremony, Queen Latifah said: "To be able to do something special for people, to change someone's life is what I was able to do tonight. I took it very seriously, I didn't enter into it lightly. It's not about TV or ratings, this was something real for me."
Clutching their gongs after the show, rapper Macklemore and producer Ryan Lewis said they were overwhelmed by their achievement.
Lewis also revealed his sister and her partner were among the couples who got married during the ceremony. "You never think you are going to win a Grammy," he said.
"It is that thing that is so distant, it's the pinnacle, it's the apex, to be able to celebrate same love. My sister getting married tonight was so personal, I still have chills now."
Macklemore said of the song: "It is a message of equality, tolerance and compassion to end homophobia, fear and hatred that has been an institution here in America.
"I thank the Grammys for giving us this platform. The fact that radio and awards shows got behind it is a testament to how far we have come."
The awards ceremony, which was hosted by LL Cool J, opened with a performance of Drunk In Love by Beyonce and Jay Z.
List of winners:
- Album of the year - Random Access Memories, Daft Punk
- Record of the year - Get Lucky, Daft Punk feat Pharrell Williams & Nile Rodgers
- Song of the year - Royals, Lorde
- Best rap album - Macklemore & Ryan Lewis,The Heist
- Best rock album - Celebration Day, Led Zeppelin
- Best R&B album - Girl On Fire, Alicia Keys
- Best country album - Same Trailer Different Park, Kacey Musgraves
- Best pop vocal album - Unorthodox Jukebox, Bruno Mars
- Best pop duo/group performance - Get Lucky, Daft Punk feat Pharrell Williams & Nile Rodgers
- Best rap/sung collaboration - Holy Grail, Jay Z featuring Justin Timberlake
- Best R&B song - Pusher Love Girl, Justin Timberlake
- Best rock song - Cut Me Some Slack, Sir Paul McCartney with Dave Grohl, Krist Novoselic and Pat Smear
- Best rap song - Macklemore & Ryan Lewis, Thrift Shop
- Best new artist - Macklemore & Ryan Lewis
- Best music film - Live Kisses, Sir Paul McCartney
- Best music video - Suit and Tie, Justin Timberlake
- Best rap performance - Macklemore & Ryan Lewis, Thrift Shop
- Best dance/electronica album - Daft Punk, Random Access Memories