After each club scored in the first round, Tambellini opened the second round with a blistering slap shot to put the Isles ahead. Evgeni Malkin followed with an unsuccessful attempt, then Kyle Okposo didn't release a shot on his chance.
Sidney Crosby could have extended the contest, but Joey MacDonald closed the door on his forehander headed for the left post with a quick pad save.
Chris Campoli and Frans Nielsen tallied in regulation for the Islanders, who were able to halt a five-game losing streak. MacDonald stopped 35 shots for his 12th win of the season and first since December 31.
Malkin and Ryan Whitney scored for the Penguins, who failed to produce a win for interim head coach Dan Bylsma, who took over when Michel Therrien was fired late Sunday.
Therrien was fired one day after the Penguins turned a 2-0 lead into a 6-2 loss at Toronto and the Pens struggling with a 27-25-5 record. He took over the club from Ed Olczyk on December 16, 2005 and led Pittsburgh to a pair of playoff berths and a trip to the Stanley Cup Finals last June.
Marc-Andre Fleury made 28 saves in defeat for Pittsburgh, which has dropped two in a row and three of their last four.
Campoli put the Isles ahead with 8:26 left in the first period, but Malkin used a defender as a screen to pump a shot past MacDonald with 1:53 to play in the opening frame.
New York took a one-goal lead with 6:34 to play in the second. Andy Hilbert took a shot from the right point which Fleury appeared to stop with his midsection. However, the puck slipped into the crease and Nielsen's second swipe put it in the net.
A little less than three minutes remained in the period when Whitney struck on the power play for a 2-2 deadlock off a dish from Crosby.
MacDonald stopped all 14 shots he faced in the third period and Fleury halted seven-of-seven
A spirited overtime which saw quality chances on both sides also failed to produce a winner.