Kovalchuk beat goaltender James Reimer from the right circle, bringing the Devils their fifth win in six games. Their lone loss in that stretch came in overtime and they are 11-1-2 over their last 14 contests.
Nevertheless, New Jersey remains 13 points out of a playoff position in the Eastern Conference.
The Devils faced a 1-0 deficit heading to the third before Dainius Zubrus tied it 3:23 into the period. Nikolai Kulemin produced Toronto's only goal at the 5:18 mark of the second.
Johan Hedberg got the win with 31 saves. Reimer stopped 37-of-39 shots. The Maple Leafs had won four of their previous five games.