A shorthanded goal by Jason Chimera 2:27 into the third period broke a 1-1 tie and Vokoun made half his 32 saves in the final 20 minutes, allowing the Capitals to halt a two-game slide. New Jersey had won three in a row.
Vokoun surrendered the first career goal by Adam Larsson with 6:54 to go in the first, but Alex Ovechkin tied it late in the second with his seventh of the year.
After Chimera put the Capitals in front, Marcus Johansson scored on a backhander with 9:17 remaining to give Washington some breathing room.
Washington opened the season with seven straight wins, but had lost four of the next six coming into Friday's contest.