Luck went 21-of-38 through the air for 228 yards without an interception and ran for a score as Indianapolis (5-2) built a 36-17 lead in the fourth quarter and then outlasted Manning's comeback try, winning for the fourth time in five games.
Darrius Heyward-Bey, Coby Fleener and Stanley Havill each made a touchdown grab for the Colts, who benefited from three Broncos turnovers, including a lost fumble by Ronnie Hillman late in the game.
Manning, who played in Indianapolis for 14 seasons, completed 29-of-49 passes for 386 yards, with three touchdowns and an interception, falling in his first game in the city since his March 2012 release from the Colts.
He was honored in a pregame video tribute and was warmly received by the Indianapolis fans.
Eric Decker hauled down eight passes for 150 yards and a score while Wes Welker and Demaryius Thomas combined for 178 yards and a touchdown on 11 catches for previously unbeaten Denver (6-1), which had a 17-game regular-season winning streak snapped.