New England (1-3-2) has not won at New York since 2007, a span of eight games.
McCarty put the Red Bulls on the scoreboard first, getting his second goal of the season in the 4th minute. He chested a cross pass from Jonny Steele onto the foot of Tim Cahill, who gave it right back to McCarty just outside the box. The midfielder put it past Revolution goalie Bobby Shuttleworth.
"At first, I was thinking, 'Tim, get out of my way,' " McCarty said. "Then two guys converged on him, so I backed away. He kneed it to me. You don't get too many that are kneed to you. It set up nicely for me and felt good coming off the foot."
New England, which hadn't scored since Jerry Bengtson's goal in a 1-0 win over Chicago in the season opener, tied it in the 6th minute thanks to an own-goal by Red Bulls defender Brandon Barklage. That snapped the Revolution's 394-minute goal-less drought.
Barklage made up for the miscue in the 9th minute with a long chip that set up Espindola for his third goal and a 2-1 lead.
"We went up and then they put some pressure on us," Red Bulls coach Mike Petke said. "It was nice we pulled it out at the end there."
Henry, who just missed scoring in the first half, scored his third goal of the season in the 82nd minute off a feed from Steele to put the game away. Steele added his first goal in the 89th minute.
"We finished it well," Henry said. "We put them under pressure from the start. It didn't look secure at one point, so we knew we had to score that third goal. That's what the whole team wanted. At the moment, we can't keep a lead, so we had to extend it."
The teams opened the game with a tribute to Boston. The introductory song was switched from the Red Bulls Anthem to "Dirty Water," a song with Boston ties as a banner in the home cheering section was read "New York Stands With Boston."
Revolution coach Jay Heaps partially blamed his team's lack of first-half focus on the bomb blasts at the Boston Marathon on Monday.
"It's a tough situation," he said. "We had six or seven guys within a half mile of the actual tragedy on Monday. We'd like to think you can step on the field and keep your focus, and unfortunately the first couple minutes was where this game was decided and our focus was not there."