Bruin scored in the 80th minute to give Houston a 3-1 lead, and his marker in stoppage time cemented it. The win snapped a two-game winless streak for Houston (5-5-5).
New York's Mike Grella opened the scoring. He took a service from Bradley Wright-Phillips at the left edge of the 6-yard box in the 42nd minute, made a quick move to the left to avoid a defender, and buried it past Tyler Deric.
Ricardo Clark made it 2-1 with his third goal of the season, volleying Boniek's corner from the far post. Bruin's first came 8 minutes later, as he made a long run, stopped and changed course at the top of the penalty area, and sailed one into the top corner past Robles.
The Red Bulls cut the deficit to one on Anatole Bertrand Abang's header as regulation time was expiring, but Bruin put it out of reach moments later with his seventh of the season.
New York (4-4-5) has lost three in a row.