Parise gave the Devils a 1-0 lead in the first period, and Michel Ouellet tied it in the second for Tampa Bay, the last-place team in the East that dropped to 1-7-2 in its previous 10.
New Jersey jumped over idle Montreal and Pittsburgh to reclaim first in the East for the first time since Feb. 29 with 84 points, one more than the Canadiens and Penguins.
Ramo was sharp in making 31 saves in his first game since a 1-0 loss to the New York Islanders on Feb. 21.
Martin Brodeur wasn't tested as much, but finished with 21 saves for his 37th win.
Ouellet had tied it 1-1 with 2:30 left in the second period on Tampa Bay's second power-play chance and just the Lightning's sixth in four games.
Dan Boyle sent a pass from the right point to the left-circle dot for a shot by Ouellet that found its way past Brodeur. Ouellet has 12 goals this season, five coming in the past seven games.
Boyle didn't see much of the third period as he received 19 minutes of penalties after punching Parise and instigating a fight 3:47 in that also earned him a misconduct. The playmaking defenseman came in with only 26 penalty minutes in 22 games this season.
The Lightning killed off the ensuing 4-minute power play, making the Devils scoreless in five advantages. Ramo was Tampa Bay's best penalty-killer, making a quick save on Brian Gionta's spin shot in front.
New Jersey had taken a 1-0 lead in the first period with a pretty passing play that finished with Parise's 28th goal and third in two games.
Gionta eluded defenseman Paul Ranger in the neutral zone and fed Elias, who rushed the puck into the Lightning's end. Elias slipped a crisp pass to Parise, who beat Ramo inside the left post with 7:44 left in the first period.
Parise scored twice in New Jersey's 4-1 win at Toronto on Tuesday that snapped the Devils' three-game skid (0-2-1).
