Eric Brewer and Richard Panik also scored for the Lightning, who have 97 points and are just one back of Montreal, which lost to the Islanders on Thursday, for the second spot in the Atlantic Division.
Anders Lindback stopped 34 shots for Tampa, which has won its past two.
Philadelphia has 91 points and is holding on to the third spot in the Metropolitan Division. The team is tied with Columbus in points, but holds the first tiebreaker for having one more win in regulation or overtime. Both squads have two games to play.
Tampa scored just two minutes in as Johnson's slap shot from the left wing on the rush beat Emery for his 24th goal of the season.
That was the only goal until 1:21 to play in the second as the Flyers tied the game after Claude Giroux's backhand pass from the left boards found Simmonds, who spun around and fired a shot in for his 27th of the season.
The Lightning took the lead back 4:33 into the third when Panik was able to put home his own rebound with a backhand from the slot, and it was a 3-1 game five minutes later on Brewer's one-timer from the left circle that went past the glove of Emery.
Philly caught a break to make it a one-goal game with 7:38 to play when Couturier's backhand feed from the right side tipped off the stick of Tom Pyatt and went in.
Tampa, though, put the game away with 5:46 to play on the power play after Stamkos' chip shot from the left side went in off the back of Emery.