The Islanders twice came back from a two-goal deficit to end a two-game skid. The Senators have dropped four in a row.
Ottawa took a 2-0 lead through one period and the Islanders came back to tie it early in a wild second stanza. The Senators then came up with goals from Bobby Ryan and Clarke MacArthur during a span of 2:13 in the second to regain a two-score advantage, but New York clawed back within one with 1:16 to go in the period on a goal from Pierre-Marc Bouchard.
Nielsen scored 3:14 into the third to tie it on the way to overtime and the shootout.
Nabokov made 27 saves to pick up the victory. Robin Lehner suffered the loss, having faced a massive 57 shots.