The Jets (2-0) scored 13 points in the second half while holding the Patriots scoreless. New England (1-1) led 9-3 at halftime.
Sanchez's scoring pass was a 9-yarder to Dustin Keller.
Feeley booted field goals from 33, 24 and 40 yards.
New England scored on field goals of 45, 25 and 29 yards by Stephen Gostkowski.
Sanchez was 14-of-22 for 163 yards.
New England's Tom Brady was 23-of-47 for 216 yards, with one interception.