The Patriots scored eight touchdowns; quarterback Tom Brady threw for three of those, including two to Gronkowski before his injury.
Aqib Talib, making his New England debut after arriving in a trade from Tampa Bay, and his fellow cornerback Alfonzo Dennard both returned picks from Colts quarterback Andrew Luck for touchdowns and Julian Edelman took a punt all the way back to the house.
Running backs Stevan Ridley and Shane Vereen went in on the ground as the Patriots ran up the score in the final quarter.
But Gronkowski's injury - apparently suffered while on the field for an extra point try in the fourth quarter - overshadowed a victory that moved the Patriots to 7-3 for the season and in complete control at the top of the AFC East.
The NFL's official website reported Gronkowski was set for surgery on Monday and is expected to miss at least a month.