On night when the Rangers were sick, when they were distracted, when it looked as if they were stepping right into an easy trap — they somehow reversed the tide and found a way. After going down 2-0 and 3-2 to the Coyotes at the Garden on Monday night, the Rangers clawed their way to a 4-3 overtime win, one that was as much will and determination as anything else. It gave them their fourth win in a row and enabled them to leapfrog the Flyers for second place in the Metropolitan Division, setting up a big game — although not quite as desperate as it would have been had they lost — on Wednesday night, when Philadelphia rides into the Garden. “We found a way,” said coach Alain Vigneault, whose team got the game-tying goal from defenseman Dan Girardi with 3:28 remaining in regulation, and then got the game-winner from another blue-liner, Ryan McDonagh, who stuffed in a rebound with 1:56 gone by in the extra frame. “We were probably a little bit not as high as we usually are emotionally, and physically, on the ice, it took us a while to get going,” Vigneault said. “It says a lot about the group.” The day started with news of both Derek Stepan and Martin St. Louis fighting the flu bug that is going around the locker room, and yet both of the forwards played — if that is the word used for their scant ice times. Stepan got 7:04 with no shifts after the 12:23 mark of the third period, and St. Louis got 11:04, stepping off at 9:12 remaining in the third and not returning. “I made a mistake tonight, I shouldn’t have played Step and Marty,” Vigneault said. “I should have taken it out of their hands. I saw it. I saw them at 4 [p.m.]. They didn’t look good. They both said they wanted to play, but at the end of the day, I’ve got to be better. I’ve got to take that out of their hands because they had no energy and obviously it showed.”