New York, 2-0 for the first time since 2011, already has 10 takeaways this season and has turned them into 31 points - a stark contrast from 2014 when New York scored 20 points off turnovers the entire season.
Indianapolis matched last season's 0-2 start by losing back-to-back games for only the second time in Luck's four-year career.
"It wasn't a pretty win, but we'll take it," receiver Brandon Marshall said. "We've got a long way to go."
Against an offense that was considered one of the league's best into the season, Revis and the Jets made sure it was no contest.
Ryan Fitzpatrick finished 22 of 34 for 244 yards with two touchdown passes and one interception - getting his first career win at Lucas Oil Stadium. Fitzpatrick became the first player since 1950 to start five consecutive road games against one team while playing for five different teams. He was 0-4 in the previous starts.
They were shut out in the first half in consecutive weeks for the first time since 1997 and Adam Vinatieri missed his first field goal inside 30 yards since 2007. And Luck was 21 of 37 for 250 yards with one touchdown and three interceptions.
"It's hard to win games in this league, even more so when we have five turnovers, 11 penalties, are 0 for 5 on third downs in the first half and can't get off the field," Colts coach Chuck Pagano said.
Pryor ended Indy's first series with a 29-yard interception return that put the ball at Indy's 9-yard line. Four plays later, Fitzpatrick found Decker for a 6-yard TD pass to make it 7-0. Nick Folk's 35-yard field goal late in the first half made it 10-0.
Indy opened the second half with a drive that lasted nearly 10 minutes and got all the way to the Jets 1 before Revis scooped up Gore's fumble.
But Fitzpatrick answered on the next series with a 15-yard TD pass to Marshall to seal the victory.
Copyright 2015 by The Associated Press