Sixteen of Thompson’s saves were made in the third period.
Arseny Gritsyuk and Timo Meier scored for the Devils (4-4-0), who won three of their previous four games. Jake Allen made 21 saves.
Gritsyuk gave New Jersey a 1-0 lead at 10:04 of the first period with a wrist shot from along the left wall that eluded Thompson one second after a power play ended.
Leonard tied it 1-1 at 16:42 with an end-to-end effort on a power play. He carried the puck up ice, split two defenders and deked Allen before sliding it across the goal line.
Ilya Protas gave Washington a 2-1 lead at 1:16 of the second period when he received a saucer pass from Alex Ovechkin on the rush and sent a wrist shot into the top far corner from the left circle.
It was Ovechkin’s 761st career assist, moving him within one of tying Nicklas Backstrom (762) for the Capitals’ all-time record.
Dylan Strome extended the lead to 3-1 with his first of the season at 4:36, scoring on a backhand at the right post.
Jenner made it 4-1 when he scored off a blocked shot in front of the crease at 11:14.
He has four goals in eight games with Washington after scoring 13 in 67 for the Columbus Blue Jackets last season.
Meier scored from the right circle on a power play with 19 seconds left in the third for the 4-2 final.