One month and one day ago, the Islanders’ season turned around in a game at the Garden. So on Tuesday night, back at the Garden, they stared down a 3-1 deficit to the Rangers and never flinched. “I really think we controlled most of the game,” said John Tavares, the Islanders star who was speaking about his team, but could have been speaking about himself, putting on a superlative performance en route to a 5-3 win. “Even though we got down two goals early, we were the better team, just stuck with it and capitalized on our opportunities when we got them.” If the Islanders are the better team, they have a long way to go before they prove it. Yet, there was hardly a better player on the ice than Tavares, who tallied three assists, making two great plays to set up Thomas Vanek’s game-winner with 4:38 remaining, and eclipsed the two goals of the Rangers’ opposing superstar, Rick Nash. “I think we know these division games for us are so big,” said Tavares, whose 62 points are second in the league only to the Penguins’ Sidney Crosby. “We dug ourselves a hole, so any time we can take a regulation win in a division game, it’s important.” That hole was hardly deeper than on Dec. 20, when the Islanders came into the Garden a beaten and beleaguered team. Yet, that day’s 5-3 win started a run of 12-5-0, getting the Islanders to 21-24-7 and once again sniffing the outside of the postseason conversation, five points out of a wild-card spot. The Rangers, now at 27-22-3, have managed to pull themselves out of their own respective hole, coming in 11-3-1 in their past 15. Nevertheless, even after Nash scored twice in opening 11:07, getting his team-leading goal total to 16 with nine in the past nine games — and even after Chris Kreider’s power play goal midway through the second made it 3-1 and wiped out a goal from the Isles’ Matt Martin late in the first — the Rangers never held the momentum in this one.