Kunitz also sent a wrist shot past Clemmensen with 3:33 to play for the eventual winner. Zach Parise drew the Devils within one in the final minute with his 24th goal.
Corey Perry assisted on both of Kunitz's goals, making an immediate contribution in his return after a four-game suspension for elbowing Philadelphia's Claude Giroux in the head Jan. 2. The Ducks were 2-2 in Perry's absence and had won just three of their last 10 games before the victory Sunday.
Jean-Sebastien Giguere made 18 saves for his first win since Dec. 14. Giguere was benched Thursday night in Los Angeles after allowing three goals in the first 21 minutes. He had not won a game (0-2-2) since making 28 saves in a 4-2 victory over Minnesota last month.
Bobby Ryan and Samuel Pahlsson also scored for Anaheim.
Ryan, a rookie winger selected with the second overall pick in the 2005 draft, has six goals in four games and has been clicking at a point-per-game pace (12 goals, 14 assists) in 26 games since being recalled from Iowa on Nov. 15.
Ducks center Ryan Getzlaf extended his current point streak to six games with an assist on Kunitz's second goal.
Bobby Holik and David Clarkson also scored for the Devils, who opened a six-game trip with a 5-1 victory in Los Angeles on Saturday.
The Ducks held a 8-1 shot advantage 12 minutes into the first period but suddenly trailed in the game when a shot from the right-point by New Jersey defenseman Mike Mottau deflected off Holik's shoulder into the Anaheim goal.
Ryan responded 2:28 later, fighting off a check from Devils center John Madden to redirect a pass from the left corner by Brendan Morrison past Clemmensen.
Travis Moen then outraced Paul Martin for a loose puck in the right-corner, centering it to Pahlsson for a goal off a one-timed shot from the slot, giving Anaheim a 2-1 lead with just 9 seconds left in the first.
The Devils tied it on a power play with 3:04 in the second period. Clarkson wrestled a rebound of Brian Rolston's shot away from Giguere's glove and swiped it in for his eighth goal of the season.