This latest win came just two days after blanking the Eastern Conference-leading Boston Bruins 1-0. Against the Sharks, New Jersey did it with goals.
Joe Pavelski, Devin Setoguchi, Jonathan Cheechoo, Patrick Marleau and Rob Blake tallied for San Jose, which wrapped up a five-game road trip with a 1-1-3 mark.
Clarkson got the game winner on the Devils' third power-play goal of the third period, the second with Joe Thornton in the penalty box.
Rolston took a shot from straight on and Clarkson got just enough of the puck so it dribbled past goaltender Evgeni Nabokov.
Scott Clemmensen, who had shutouts in his past two starts, had to made two saves on a late Sharks' power play to preserve the win, his 25th of the season, the second-most by any Devils goaltender.
The games between two of the NHL's top defensive teams was hardly what anyone expected with the teams combining for 11 goals on 61 shots.
The Devils led 3-2 after the first, trailed 4-3 after the second, went in front 5-4 early in the third only to see Pavelski tied the game with a short-handed goal with less than 10 minutes to play on a great individual effort.
He picked up a turnover at center ice, skated around Rolston and backhanded a shot into the top corner past Clemmensen.
Elias and Langenbrunner put the Devils ahead with power-play goals set up by Zach Parise. Elias tied the game at 4-all on a two-man advantage and Langenbrunner got his 10th in the past 15 games on a rebound 3 minutes later.
Setoguchi had given the Sharks a 4-3 lead in the closing seconds of the second period, scoring on a two-man advantage. Cheechoo had tied the game at 3-all with a slap shot from the right circle.
While the Sharks and Devils came into the game ranked among the league's top four in goals against, the first period was anything but defensive with five pucks finding the back of the net as New Jersey took a 3-2 lead.
An early giveaway in the San Jose zone allowed Gionta to tip a shot past Nabokov 30 seconds after the opening faceoff.
Blake tied the game about 4 minutes later with a blistering slap shot after a New Jersey turnover.
Rolston scored in close around the 8-minute mark on a nice setup by John Madden, but Marleau tied the game less than a minute later, getting his 30th of the season on a deflection during a power play.
Clarkson gave the Devils the lead with a turnaround shot from between the circles that Nabokov had a hard time seeing with Madden in front.
