Kelce -- wearing a sharp double-breasted suit -- had the crowd laughing from start to finish ... with jokes about getting busted for weed in college, his infamous dating show, his QB's unique voice and, of course, beating his older brother, Jason, in the Super Bowl.

The Philadelphia Eagles star was in the front row for the whole thing ... and cameras even cut to him multiple times as Travis talked about growing up together.

"Jason and I have actually been playing football together since we were little kids, and he was always better than me at everything," Kelce said.

"In high school, he was an honor student, and I got kicked off the team because I failed French ... and English too, but French sounds way better."

"Then when we were in college, I actually got kicked off the team because I tested positive for marijuana. So, it just goes to show you if you smoke weed and you're bad at school, you can win the Super Bowl twice."

Travis' family -- including Mama Kelce -- were also present for the monologue.

Kelce explained it was an emotional moment for him ... as he grew up watching Will Ferrell and Adam Sandler on the same stage.

Jason also made an appearance in a skit later in the show ... just as 'SNL' producers previously told us they were trying to make happen.