Kyle Okposo and Blake Comeau scored on the Islanders' first two shootout attempts against Henrik Lundqvist, but Nigel Dawes and Fredrik Sjostrom tied it.
In the fourth round, Park beat Lundqvist again before Wade Dubielewicz turned aside Petr Prucha. Dubielewicz made 48 saves, and Lundqvist stopped 29 shots before the shootout.
The Islanders earned a split of the home-and-home series with their archrivals, but didn't meet their prime objective of spoiling the Rangers' postseason plans. The Rangers locked up an Eastern Conference playoff berth with a 3-0 victory on Long Island on Thursday night.
All that remains on the line for the Rangers is a chance to finish fourth in the East and have home-ice advantage over the New Jersey Devils in the first round of the playoffs. The Rangers and Devils close the regular season Sunday in New Jersey.
After reaching the postseason in four of the previous five seasons, the Islanders (35-38-9) can now set their sights on Monday's NHL draft lottery with the hope of winning the chance to pick first in June.
The Islanders took three one-goal leads, the last on Park's 12th of the season just 7 seconds into the Rangers' long 5-on-3 power play. The Rangers got a full 2-minute advantage when Josef Vasicek was sent off for cross-checking, and defenseman joined him in the box for unsportsmanlike conduct.
The Rangers got 10 shots, but had nothing else to show for that power play except another one-goal deficit.
Okposo scored his second NHL goal in the first period, and Miroslav Satan netted his 16th of the season in what might have been his final Islanders game. Satan, finishing his third season with the Islanders, can become an unrestricted free agent this summer.
Dan Girardi and Dawes both scored tying goals in the second period for the Rangers, who outshot the Islanders 21-10 in the second and finished with a season-high 51.
Okposo, in his ninth NHL game, added Lundqvist to his list of NHL goalie victims that until Friday consisted of only New Jersey's Martin Brodeur. He took a pass from Blake Comeau and made it 1-0 at 10:10.
Girardi tied it 2:29 into the second, but Satan put the Islanders back in front 3:11 later. Dawes' shot hit the skate of Islanders forward Trent Hunter and sailed past a surprised Dubielewicz at 13:10 before Park tied it with 4:53 left in the second.
