Parise won it with his 20th goal, tipping a drive by Patrik Elias past Ty Conklin on the only shot of overtime. New Jersey, Pittsburgh and Philadelphia all have 63 points in the five-team Atlantic.
Martin Brodeur earned his 28th win of the season and was credited with an assist on the winning goal. That made up for his tripping penalty in the third period that led to Jordan Staal's power-play goal.
The Devils, who recorded only 14 shots through two periods, mounted a quick comeback in the third that they didn't seem to have in them through another lackluster home performance.
After Staal pushed Pittsburgh's lead to 3-1 4:30 into the final period, Elias and Clarkson connected 1:44 apart.
Elias got the rally going at 9:37 when he sent a shot toward the net that hit defenseman Kris Letang in front and caromed past Conklin. Clarkson tied it with his seventh of the season and second in two games, getting to a rebound of Johnny Oduya's point shot and popping it in at 11:21.
That finally gave the record-low crowd of 13,012 fans at the new Prudential Center something to cheer about. Until then, the loudest roar was in the first period when the Devils posted a congratulatory message on the scoreboard to the Super Bowl champion New York Giants.
Each club had 10 shots in the third period and both seemed content to play conservatively and get to overtime.
The road team had won an NHL-record tying nine straight in this series, including the first five this season with New Jersey winning three times in Pittsburgh. The Penguins extended the run last Tuesday by beating the Devils 4-2 in Newark.
Petr Sykora and Ryan Malone also scored for the Penguins, who fell to 3-2-2 since Sidney Crosby's ankle injury.
Evgeni Malkin had two assists to tie Crosby for the team lead with 63 points.
The Penguins snapped the scoreless deadlock when Malone connected for the fifth time in six games 2:26 into the second period.
Pittsburgh nearly doubled its lead during power play No. 4, but referee Don Koharski immediately and emphatically ruled that Erik Christensen kicked the puck past Brodeur just over a minute later.
That elusive second goal did come with 8:10 left in the period when Sykora took a pretty pass that Malkin sent through his legs over to his fellow forward. The former Devils player carried the puck between two defenders and let a shot go from above the left circle. It was Sykora's 17th goal this season and 600th NHL point.
Langenbrunner, who sat out last Tuesday's matchup with the Penguins because of the flu, cut the deficit to 2-1 with 41.7 seconds left in the middle period.
