The Rangers' Adam Fox leaves the ice during the third period...

The Rangers' Adam Fox leaves the ice during the third period after an injury against the Tampa Bay Lightning at Madison Square Garden on Saturday. Credit: Jim McIsaac

The Rangers, who have struggled so frequently at Madison Square Garden this season, lost another home game Saturday afternoon.

And that might not have been the only thing they lost.

With 12:57 left in the third period of their 4-1 loss to the Tampa Bay Lightning, defenseman Adam Fox, their co-leading scorer and top power-play point man, left for the locker room and did not return.

Coach Mike Sullivan said Fox was being evaluated for an upper-body injury.

In the meantime, the Rangers (13-12-2), playing the second game of a back-to-back, saw their home record fall to 2-8-1 and their winning streak end at three games.

Brandon Hagel had two goals for Tampa Bay (16-7-2), Nick Paul added an insurance goal early in the third period and Jake Guentzel scored into an empty net with 17.4 seconds left to seal it.

Igor Shesterkin, playing for the second straight day after backstopping Friday afternoon’s 6-2 win over the Bruins in Boston, stopped 31 of 34 shots to keep his team in it. The Rangers were outshot 35-12.

“We did it to ourselves,’’ said a disgusted J.T. Miller, whose goal late in the second period cut the Lightning’s lead to 2-1. “There was no urgency today. We dipped our toe into the game, got outplayed basically the whole time. It’s unacceptable. We’re trying to develop a standard and an identity around here, and that was certainly not it.’’

Said Sullivan, “We got outcompeted from the drop of the puck.’’

The Rangers played their ninth game in 15 days, but Mika Zibanejad said that was no excuse for their effort.

“No. I don’t think that’s something that we think about or have in our mind,’’ he said. “We know the schedule, and it’s pretty much the same for everyone at some point. That’s not an excuse for the game today.’’

The Rangers were outshot 9-0 to start the game and 11-2 in the first period. They fell behind 1-0 on Hagel’s first goal at 10:53, but Shesterkin kept them in it.

Hagel’s second goal, on a breakaway at 8:57 of the second period, made it 2-0, but Miller redirected a pass from Fox to get them on the board at 17:31.

Right after that, the Rangers had some jump and seemed to get some pressure on Lightning goalie Jonas Johansson. But a penalty to Shesterkin with 18.1 seconds left in the period — he was called for interference against Hagel as he cut through the goal crease to chase the puck — ended that.

The Rangers killed the penalty, but shortly after it ended, Paul got free at the goal crease to bang in a feed from Nikita Kucherov and make it 3-1 at 2:02 of the third. And that was a downer for the Rangers.

“Yeah, it was,’’ Sullivan said. “It was because ... they obviously have a dangerous group there [on the] power play, and we kill it off, we get back to five-on-five, and then they get one off the rush there. You know, just attention to detail. We have numbers back and we just don’t defend it the right way.’’

The Rangers got a power play with 8:04 left but didn’t have Fox to run the point. They chose to use a five-forward power play, with Artemi Panarin running the point and Will Cuylle joining the group to play at the net front. But they couldn’t score.

“He’s a Norris [Trophy-winning] defenseman,’’ Zibanejad said of Fox. “He’s been running our power play for so long. So I think when that happens that quickly, you’re just trying to simplify things. You try to find ways just to get pucks to the net and not to try to over-complicate things. And we had some looks. But obviously it’s a different type of power play when he’s not on there.’’

Miller had praise for Shesterkin’s efforts but was annoyed with the team’s effort overall.

“Just will. And determination,’’ he said when asked why the Rangers couldn’t fight back after a poor start to the game. “And they were more willful than we were today. They were ready to go into every battle.

"They won every battle, it seemed like, for 30 minutes. We had a good 10 minutes, I think, there in the second. We had some momentum, the building came back alive a little bit. We get the kill, and then give up another one, and it’s deflating. At no point in that game were we deserving of winning.’’

Notes & quotes: Defenseman Will Borgen came off injured reserve and returned to the lineup after missing five games with an upper-body injury ... Ds Urho Vaakanainen and Scott Morrow and forward Conor Sheary were the scratches.

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