Sidney Crosby had assists on all three goals for Pittsburgh, which extended its winning streak in the series to eight games. Pittsburgh halted Tampa Bay's bid to tie a club record with an eighth consecutive triumph on home ice.
Kunitz opened the scoring seven minutes in, taking a pass from Crosby and lifting it past Lightning goalie Ben Bishop from the left circle. Kunitz sealed the win with an empty-net goal with 1:43 remaining in the game.
Brandon Sutter scored the second Pittsburgh goal on a power play midway into the third period. Sutter took his own rebound behind the net and banked it off the skate of Lightning defenceman Victor Hedman on the opposite side.
Tampa Bay had several excellent scoring chances. Richard Panik got loose in front of the Pittsburgh net just before the second intermission, but was rejected by Fleury, who earlier stopped Nikita Kucherov on a partial breakaway.
The Lightning also came up empty in three man-advantage situations.
Bishop, who finished with 26 saves, has lost twice in his last three games despite stopping all but three of 107 shots.
NOTES: Crosby, Kunitz and Evgeni Malkin each have seven-game point streaks against the Lightning, with a combined 23 goals and 22 assists. . Tampa Bay is 0-6 in games when it trailed after the first period. . Pittsburgh broke a tie with Tampa Bay for second place in the Eastern Conference. . Penguins LW Chris Neal was held without a point for the first time in six games, having collected 11 on six goals and five assists in his past five outings.