The loss, coupled with the Rangers' 2-1 escape over Buffalo, enabled New York to clinch second place in the Metropolitan Division. The Flyers cannot finish higher than third.
The Flyers got to within 3-2 when Sean Couturier's pass was inadvertently deflected into the net by Tampa Bay's Ondrej Palat with 7 minutes, 38 seconds left. But less than two minutes later, Steve Stamkos' power-play goal secured the victory.
The Flyers, who again were badly outplayed in the third period, have lost six straight in Tampa since 2011.
Tampa took a 2-1 lead as Richard Panik scored on his own rebound, backhanding a shot past Ray Emery with 15:27 to go in regulation. With 10:17 remaining, defenseman Eric Brewer broke free from Steve Downie and scored from the left circle for his second goal of the season, giving Tampa a 3-1 cushion.
"I've got to make saves in the third period," said Emery, who stopped 26 of 30 shots in the game.
Simmonds was unhappy with the team's final period.
"We've been playing great in the first 40 minutes, but for some reason we don't play the complete ," he said.
Scott Hartnell added, "A 1-1 game going into the third, you've got to win those games if you're going to go far."
If the Flyers finish third, they will face the Rangers in the first round of the playoffs, with New York having the home-ice advantage.
The Flyers are tied for third place with Columbus with 91 points, and both have two games remaining. The Flyers have the tie-breaker - most wins in regulation and overtime, 38-37.
The Flyers are assured of a playoff berth. If they finish behind Columbus and drop into a wild-card spot, they would face Pittsburgh or dreaded Boston in the opening round.
Columbus' games are at Tampa and Florida. The Flyers conclude the regular season by playing in Pittsburgh on Saturday and hosting Carolina on Sunday.
"We just have to keep scrapping around," Simmonds said before the game. "We have to work on our consistency and our overall play and make sure we're in a good spot going into the playoffs. We want to be going in on a high note, not a low note."
Simmonds' power-play goal with 1:21 left in the second period knotted the score at 1-1.
Alone in front, Simmonds scored on a spin-around shot that bounced off Lindback and into the net. It was his 16th power-play goal, third in the NHL.
Lindback, thrust into action against Toronto on Tuesday because of an injury to standout starter Ben Bishop, had not allowed a goal in almost 95 minutes before Simmonds' tally, stopping 51 shots over a two-game stretch.
The Flyers were relentless in the final five minutes of the second period, coming in waves at Lindback, who made a key stop on Adam Hall's shorthanded breakaway about two minutes before Simmonds' goal.
Earlier in the period, Tampa Bay hit the post twice while it held a 1-0 lead.
After a ragged start, the Flyers regrouped and had the better scoring chances in the last half of the opening period, but they couldn't solve Lindback, who didn't resemble the goalie who took a 6-12-2 record, 3.11 goals-against average, and .884 save percentage into the game. He has three of his seven wins this season against the Flyers
After the morning skate, Flyers winger Scott Hartnell said Lindback and Bishop were "similar goalies. They're 6-6 or 6-7, and they take up a lot of the net. You just have to get people in front of them and make their life stressful."
Two minutes into the game, Tampa Bay, which is trying to overtake Montreal in a battle for second place in the Atlantic Division, took advantage of a neutral-zone turnover by Downie. Tyler Johnson took a pass from Stamkos and one-timed a blast from the top of the left circle past Emery.
It was Johnson's 24th goal, the most ever scored by a Tampa Bay rookie.