The Atlantic Division champion Penguins have a five-point lead over Montreal for the top seed in the conference.
The Penguins are still without center Sidney Crosby (broken jaw), left wing James Neal (concussion) and defenseman Paul Martin (hand). Defenseman Kris Letang was back in the lineup and had an assist after missing the previous six games with a lower body injury.
"It was fun to be part of a match and with the win, it makes it even better," Letang said.
Pittsburgh has a six-game winning streak against the Lightning.
"That's a really good team," Tampa Bay coach Jon Cooper said. "That's a team that has won 15 games in a row in the top league in the world."
Early third-period goals by Malkin and Jokinen gave the Penguins a 5-2 lead. Glass got his first goal in 56 games during a late third-period power play.
"For me, it was just a relief," Glass said. "I think the bench was happier than I was, but look out now. The floodgates are open, so I hope I have a few more of those."
Kunitz put Pittsburgh up 3-1 with a redirection on the power play early in the second period. But Connolly stopped a personal 54-game goal drought dating back to Nov. 17, 2011 against Pittsburgh, when he got Tampa Bay within 3-2 with a man-advantage goal.
The Penguins had taken a 1-0 lead 4:07 into the game when Jokinen scored from near the post on a rebound. Dupuis made it 2-0 during a power play on another rebound goal.
"They did a good job of just getting to the net," said Tampa Bay goalie Ben Bishop, who made 35 saves.
After Malkin was called for tripping while battling for position in front of the Tampa Bay net, Purcell cut the Lightning deficit to 2-1 from the right circle. He connected off a pass from Steven Stamkos on the ensuing power play.
Purcell scored another power-play goal in the final minute of the game.
The chippy game had a total of 23 penalties, including two fighting majors, a 10-minute misconduct and 10 roughing minors.
Crosby missed his fifth consecutive game. Neal has been out the past two games. Martin, sidelined six straight games, has resumed skating on his own. ... Tampa Bay D Victor Hedman missed his fourth game due to a lower body injury, but could return this weekend. ... Malkin got his 556th point on his goal, which moved him past Kevin Stevens into seventh place on the Penguins' career list.
Copyright by STATS LLC and The Associated Press
TAMPA, FL - APRIL 11: Ryan Malone #12 of the Tampa Bay Lightning skates prior to a game against the Pittsburgh...