The win was the third in a row for the Pacers, who now trail Boston and Brooklyn for eighth place in the Eastern Conference by one game. C.J. Miles added 13 points for Indiana, which improved to 2-0 with Paul George in the lineup. George provided 10 points in 16 minutes off the bench after finishing his season debut on Sunday with 13 points.
Roy Hibbert recorded a double-double with 11 points and 11 boards in 16 minutes.
Pacers had lost three straight road games heading into Wednesday's contest.
The Knicks were limited to 5-of-20 shooting from the floor in the opening stanza and trailed 26-14 after 12 minutes of play. Hibbert tallied seven points and six boards in the first period.
Indiana connected on 60 percent of its field goal tries in the second quarter, assisting on seven of its 12 makes en route to a 54-38 halftime lead.
After Galloway opened up the second half with a jumper on New York's opening possession, the Pacers responded with a 10-0 run.
The Knicks narrowed the deficit with a 13-3 run to begin the final frame, but Indiana scored seven of its 17 fourth-quarter points from the free throw line.
Indiana was without forward Chris Copeland, who was stabbed outside of 1 OAK club in New York City nightclub early Wednesday morning. Copeland suffered a knife wound to his left elbow and abdomen, but is in stable condition at a nearby hospital.
The Pacers finished with a 54-34 advantage in total rebounds.
C.J. Watson missed his second consecutive game with a sore elbow ... With the win, the Pacers completed the season-series sweep of New York ... The Knicks have lost six of their last seven games at Madison Square Garden ... Jason Smith, Tim Hardaway, Jr. and Quincy Acy all had 12 points off the bench for New York ... David West made all five of his field goal attempts for 11 points for the Pacers.