Tarasenko pushed it to 4-1 at 4:01 of the third period when he buried the rebound of Brady Tkachuk's shot on a 2-on-1 into an open net.
"We got off to a good start with a few early goals," Forsberg said. "At the end, I thought we played very mature and we had some big blocks in there. The guys fought hard. It was fun to watch."
Point scored 35 seconds later from the low slot off a centering pass by Brandon Hagel to make it 4-2.
"You can't get this back. There goes an opportunity to get points," Lightning coach Jon Cooper said. "Everybody around you won today and you didn't. We can't be doing this win one, lose one or win two, lose two. ... That's not going to get it done for us."
NOTES: Kucherov played in his 700th NHL game. ... Giroux has seven points (three goals, four assists) during a five-game point streak. ... Hagel extended his point streak to 10 games (seven goals, eight assists). ... Senators defenseman Artem Zub had two assists. ... The Lightning held a moment of silence before the game in remembrance of Mason Fox, who had participated in their Hockey Fights Cancer night on Nov. 30.