New York overcame the return of the Penguins' Sidney Crosby as well as a two-goal deficit to grab home-ice advantage in the Eastern Conference quarterfinals.
The Islanders will host the third and fourth games in the series Sunday and Tuesday.
The top-seeded Penguins overwhelmed New York in the series opener 5-1 and Pittsburgh took a 3-1 lead after one period Friday -- Crosby scoring twice in the opening stanza.
Crosby was cleared to play for the first time since March 30 after recovering from a broken jaw.
The Islanders began their comeback with a goal from Colin McDonald 5:12 into the second period and Matt Martin tied it 4 minutes later.
It remained a 3-3 contest until Okposo beat Marc-Andre Fleury.
Evgeni Nabokov earned the win with 30 saves. He has 41 post-season victories in his career, but this was his first in three seasons as well as his first for the Islanders. He spent his first nine years of his decade-long career with San Jose.