Wolski came in slowly on Flyers goalie Sergei Bobrovsky and moved to his forehand at the last moment, sliding the puck along the ice and into the corner of the net.
Erik Christensen also scored in the tiebreaker and Henrik Lundqvist stopped Nikolay Zherdev to hand the Rangers a much-needed win as they battle to secure an Eastern Conference playoff spot.
New York came into the game clinging to the eighth and final post-season seed in the East.
Bryan McCabe and Ruslan Fedotenko scored in regulation and Lundqvist stopped 32-of-34 shots for the Rangers.
James van Riemsdyk and Zherdev notched goals and Bobrovsky made 32 saves for the Flyers, who pulled into a tie with Washington for the top seed in the East with three games to play.