Taylor Swift and Travis Kelce are hoping the Cleveland Cavaliers will avoid a heartbreaking playoff defeat and subsequent 'Cruel Summer' ... showing up courtside for Game 3 of the Eastern Conference Finals.

The pop star and her NFLer fiancé pulled up to Rocket Arena in Cleveland, Ohio to cheer on Travis' hometown basketball team as they try and fight back from a 2-0 deficit in the series against the New York Knicks.

In one particularly sweet moment, Swift coverly slipped Kelce a stick of gum ... gotta keep that breath minty fresh, fella.

The two seemed to be enoying themselves ... chatting about something Taylor pointed out across the court.

Taylor and Travis' entrance drew eyes ... people pointed as the two megastars made their way to their seats -- surrounded by security.

Kelce -- ever a man of the people -- got the crowd hyped up before sitting down.

As yoiu know ... Travis is from Cleveland Heights -- an East Cleveland suburb -- and he regularly roots for his hometown teams like the Cavs and Cleveland Guardians.

The two -- who were spotted having dinner in New York City just last night -- are rapidly approaching their wedding date ... with Taylor even making personal calls to A-List guests to give them the 411 on the event.

The Knicks are leading the Cavs at the end of the first quarter ... we'll have to wait and see if these stars can motivate the squad to come back!