Urruti also had an assist, as the Impact improved to 1-9-0 all-time on the Red Bulls' home turf. Defender Zakaria Diallo also scored his first goal of the season for Montreal (6-4-2, 20 points).
Defender Aaron Long scored his first of the season for the Red Bulls (3-5-2, 11 points).
The Impact received the penalty kick after forward Anthony Jackson-Hamel was knocked to the ground in the box by Long.
Urruti lined up the shot and sent a low kick into the right corner of the net as New York goalkeeper Luis Robles guessed in the other direction. The goal was Urruti's first of the year after he scored 29 for FC Dallas over the past three seasons.
The goal gave Montreal the breakthrough it craved. The Impact have been outscored 29-10 in 10 meetings at Red Bull Arena after the win.
Montreal standout midfielder Ignacio Piatti (knee) sat out for the ninth consecutive game.
Red Bulls forward Bradley Wright-Phillips (groin) missed his third straight game.
The Impact had a 10-5 edge in shots and put four on target compared to two for New York.
The Red Bulls broke a scoreless tie in the 36th minute.
Midfielder Marc Rzatkowski took a free kick and sent a left-footed boot into the box. Long was stationed in front of the net and headed the ball past Montreal goalkeeper Evan Bush for a 1-0 lead.
The Impact knotted the score in the 64th minute on a sequence that began with a corner kick.
Midfielder Omar Browne took the corner and passed the ball to nearby Urruti, and the veteran forward threaded a liner toward the net. Diallo deflected the ball with the side of his head, easily sending it past Robles.
Long had a chance to score his second goal in the 75th minute, but he sent his header from the center of the box to the right of the goal.
Four minutes later, Long set up Montreal's game-winning goal with his foul.
Montreal profit from late penalty against Red Bulls
New York's goalscorer Aaron Long went from hero to villain when he conceded the penalty Maxi Urruti needed to see Montreal win 2-1.
Urruti converts Montreal penalty conceded by Aaron Long
Major League Soccer: Maximiliano Urruti (79' PEN) New York Red Bulls 1-2 Montreal Impact
Long's header puts the Red Bulls in front
Major League Soccer: Aaron Long (36') New York Red Bulls 1-0 Montreal Impact