The Dutchman scored his eighth goal in 10 games this season.
Forward Nick Soolsma opened the scoring for Toronto (6-13-15), which has given up a league-worst 59 goals.
Midfielder Monsef Zerka and forward Milton Caraglio scored for New England (5-16-13).
Caraglio’s goal came one minute into the second half and looked to be enough for a New England win until Koevermans tapped in a long ball from substitute Gianluca Zavarise.
Benny Feilhaber set up both goals for New England.
Entering the game, Toronto had lost just once in its last six MLS games and was 3-2-5 in its last 10.
New England had lost five straight and not won in league play since Sept. 10 under coach Steve Nicol.