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Taylor Swift Brings Travis Kelce on London Stage ... Tuxedo On, Skit Ready!!!

Taylor Swift's mixing business and pleasure -- finally bringing Travis Kelce out onstage with her in London Sunday ... and, we gotta say he nailed the choreography.

The singer-songwriter took the stage in England's capital Sunday -- her third show this weekend -- and, her footballer boyfriend went from spectator to spectacle ... hitting the stage in a tuxedo and top hat.

This all went down during "The Tortured Poets Department" part of her set ... as part of the intro for "I Can Do It With a Broken Heart" she pretended to throw a tantrum and collapse to the stage.

Of course ... her better half had to come and rescue her -- picking her up and carrying her to a heart-shaped bed while jovial, upbeat music played.

Check out the clip ... he drops her on the bed before fanning himself while the other two guys in tuxedos continue to care for T-Swift -- and Travis helps encourage her to get back at it with some of his silliest dance moves.

Ultimately, Taylor decides to bravely continue ... and Travis gives her makeup a touchup before running offstage.

Of course, Travis has supported Taylor at every show this weekend ... including Friday when he brought his big bro Jason and sister-in-law Kylie to watch and yesterday when he got chummy with movie star Tom Cruise.

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This, however, is the first time he's ever gotten involved in the show despite attending many of her concerts since they started dating ... and, if you listen to the applause -- fans absolutely loved it.

Travis has to head back to Kansas City soon to start gearing up for football season ... so, unclear when he'll get a chance to attend another Taylor show.

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But, clearly Swifties want him to know he's always a welcome sight onstage.

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