Malkin, making his return after missing four games due to a concussion, tied it 5:38 into the third period on a pretty breakaway. Crosby put Pittsburgh in front moments later with a slap shot from the slot that zipped past Anders Lindback and into the net.
Tampa Bay's Steven Stamkos scored twice to push his league-leading total to 17, but it wasn't enough to stop the Lightning's slide.
Marc-Andre Fleury helped shore up a leaky Pittsburgh defence by making 24 saves as the NHL's two highest-scoring teams kept things in check until the third period.
Tampa Bay starting goaltender Mathieu Garon left early in the second period with a lower-body injury, pressing Lindback into action. Lindback stopped 16 shots, but was overmatched when two of the league's best players put on a show early in the third period.
Malkin, activated Monday morning after passing all of the league-mandated concussion protocols, tied things with his fifth, and undoubtedly most spectacular, goal of the year.
The league's reigning MVP took advantage of a Tampa Bay turnover and raced in from the right side. He darted to the middle and between a pair of sliding Lightning defenders before slipping the puck into an open net. The Russian let loose a massive fist pump in celebration, though the roar would only get louder 117 seconds later.
The Penguins used the momentum from Malkin's goal to put together an odd-man rush, with defenceman Kris Letang deciding to hold onto the puck and circle the net. He then fed Crosby with a perfect cross-ice pass that Crosby blasted by Lindback to put Pittsburgh in front.
Fleury and a defence that played more responsibly than it has of late made it stand as Tampa Bay fell to 0-6 at the Consol Energy Center during the regular season.
Pittsburgh allowed the Lightning one power play and kept Tampa Bay in check for long portions — save for a brief breakdown in the second period. Stamkos scored from the front of the net when the Penguins decided to leave him by himself on the doorstep.
The goal tied it 1-1 and Tom Pyatt put the Lightning ahead with just over 8 minutes to play in the second period. Nate Thompson's wrist shot from between the circles smacked Pyatt in the face before floating softly over the head of Fleury, who was on his knees and never moved until the red light came on.
The Lightning, who blew an early two-goal lead in a loss to Boston on Saturday, again faltered in the third while Pittsburgh continued its mastery of Tampa Bay — at least during the regular season.
NOTES: The Penguins scratched D Paul Martin, who remains day to day with a lower body injury. Pittsburgh also scratched LW Zach Boychuck and D Robert Bortuzzo ... Tampa Bay scratched D Brendan Mikkelson and D Marc-Andre Bergeron ... Pittsburgh is off until Thursday, when it plays at Philadelphia, while the Lightning play in New Jersey on Tuesday.
Follow Will Graves at www.twitter.com/WillGravesAP