The Devils have won two in a row on the heels of a four-game skid. They will try for their first three-game winning streak since mid-December when they play in Philadelphia Saturday.
A shorthanded goal by Mathieu Darche 1:35 into the middle period gave the Canadians a 3-1 lead but Clarkson scored on the power play with 6:17 to go in the stanza to begin the New Jersey comeback.
Dainius Zubrus tied it 6:11 deep in the third and Parise put the Devils in front on a slap shot with 2:44 left in regulation. Parise also scored midway through the first period.
Clarkson added an empty-net goal with 32 seconds left, his 19th goal of the season.
Martin Brodeur stopped 27 shots to get the win, the 641st of his career. Carey Price allowed four goals on 21 shots.