The Broncos (6-1) saw their 17-game regular-season winning streak snapped. With a victory on Sunday they would have tied the 2003-04 New England Patriots for the third-longest regular-season win streak in NFL history.
Instead, Denver's loss left the Kansas City Chiefs (7-0) as the league's only unbeaten team.
Manning won four MVP awards and a Super Bowl title in 13 years with the Colts before they allowed him to become a free agent. The move cleared the way for Indianapolis to select Luck with the first pick of the 2012 draft.
The Colts honored Manning before the game with a video presentation and crowd applause before Manning passed for 386 yards and three touchdowns, completing 29 of 39 passes in his first game against them. He was intercepted once.
"There's no question that was emotional during that tribute," Manning told reporters. "I felt probably a little tired coming into this week. I'm kind of, in some ways, somewhat relieved this game is over."
Denver's Eric Decker had eight catches for 150 yards and a score.
Luck went 21-for-38 for 228 yards and ran four times for 29 yards for the Colts (5-2).
"I have never looked at it as the guy that replaced Peyton.
I just looked at it as a chance to play football for a great team," Luck said.
"We didn't let the outside sphere of influence creep into the locker room, which is a testament to the guys."
The Broncos lost despite outgaining the Colts 429 yards to 334. Denver turned the ball over three times, while Indianapolis only gave it away once.
The Colts scored the final 16 points of the half to take a 26-14 lead into the locker room and were ahead 36-17 in the fourth quarter where Manning nearly engineered one of his famous rallies.
His 31-yard touchdown pass to Demaryius Thomas with 12:11 left cut the Colts' lead to 36-23. Another scoring drive made it 36-30 but Manning was intercepted on his next possession and Broncos running back Ronnie Hillman fumbled away their next drive at Indianapolis' 2-yard line.
It was not all positive for the home team, as Indianapolis receiver Reggie Wayne left the game in the fourth quarter with a sprained right knee and did not return.