The Senators, on the second end of a back-to-back, snapped a five-game losing streak on Monday night with a 2-1 win over Pittsburgh. The recent downturn has pushed Ottawa (34-31-5, 73 points) six points behind Florida for the second wild card spot in the Eastern Conference.
After winning the first two games against the Bruins this season - both on home ice - the Senators fell to Boston, 3-1, on Feb. 20 at TD Garden.
"I think they won [on Monday night], so they're probably feeling pretty good about themselves," said Grzelcyk. "Every game probably feels pretty close to a playoff game and they haven't been there in a few years. They've got a lot to prove and they've got a lot of young talent…a good power play.
"We've got to stay disciplined, something we've lacked in a little bit recently. I've got to be mindful of that and I don't want to give them any easy opportunities. And they played last night, so get on them early and make them work for it."
Ottawa is paced by Tim Stutzle, who leads the club with 35 goals and 78 points in 66 games. Brady Tkachuk (30-42-72) has also hit the 30-goal, 70-point plateau, while Claude Giroux (28-30-68), Alex DeBrincat (21-35-56), and Drake Batherson (21-34-55) have reached the 20-goal mark.