After Tampa Bay's Steve Downie had scored twice within 11 seconds to hand the Lightning an early 2-0 lead, but Malkin began a Penguins comeback that saw them rack up four answered goals.
His power-play tally late in the first period halved the Pens' deficit, and Chris Kunitz scored the equalizer only 56 seconds into the middle frame.
Kris Letang's marker 3 1/2 minutes later put Pittsburgh ahead and Malkin's 32nd goal of the year capped the run.
The Penguins' center boosted his point total to an NHL-best 69 with the performance.
Mathieu Garon yielded four goals on 41 shots for Tampa Bay.