After allowing a shorthanded tally by Buffalo, the Penguins made sure they took advantage of their power-play opportunities, erupting for four straight man-advantage goals.
Wayne Primeau and Alexandre Daigle cashed in on first-period chances before Aleksey Morozov and defenseman Michal Rozsival tallied in the second for Pittsburgh, which snapped a three-game winless skid.
The Penguins, who were four for 30 with the man advantage at home entering the game, scored four power-play goals for the first time since netting five on Dec. 30, 1999 against the New York Islanders.
Kovalev capped the scoring 43 seconds into the third period with his seventh goal of the season, all in the last five games.
Pittsburgh's Mario Lemieux extended his assist streak to seven games with two, giving him at least one assist in every contest since the season opener.