The Kansas City Chiefs star and his big brother, Jason, were at their old stomping grounds to film a live episode of their 'New Heights' podcast ... and when it came time to put a bow on the festivities, officials at their alma mater surprised them with an impromptu commencement ceremony.

Both dudes had previously graduated from the school ... but neither got to walk across the stage to snatch their diplomas -- so the moment was pretty special for the two.

And, just before Travis got ahold of his official paperwork ... he just had to chug a brew to memorialize the occasion -- before he spiked the can right on the stage.

More fun, of course, was had throughout the night ... including when the brothers played a "Name That Tune" game with fans in attendance. The band began playing Taylor Swift's familiar "Shake It Off" notes ... and once Travis caught the melody, he began dancing his tail off to the song.

One of the contestants eventually correctly guessed it was Swift's ditty -- prompting Travis to scream into the mic, "One of my favorites right there, ladies and gentlemen. All right, now!"

The guys were ultimately joined by Joe Burrow and Orlando Brown once they sat down to film the pod ... and, yes, a little Chiefs-Bengals smack talk did happen.