Luck hooked up with Reggie Wayne on the Colts' second possession and T.Y. Hilton hauled in a scoring strike early in the second quarter for a 17-3 lead.
The Indianapolis signal-caller finished 9-of-13 for 107 yards as the Colts notched their first exhibition win.
New York's Eli Manning also played into the second quarter, going 8-of-17 for 91 yards with an interception.
Hakeen Nicks made his first pre-season appearance for the Giants and made two 20-yard receptions, setting up two Josh Brown field goals.