Angel's 16th goal this season gave New York a win, a loss and two ties in its last four games.
The draw prevented New England from sweeping the season series with the Red Bulls (11-10-5) for the first time in eight years.
Francis Doe scored New York's first goal in the 37th minute.
The Revolution (13-6-7) got goals from Taylor Twellman in the 22nd and 70th minutes, and remained in second place in the Eastern Conference behind front-running D.C. United.
New England had won five in a row against the Red Bulls.