Nick Schmaltz had a goal and an assist, Clayton Keller had two assists, and Scott Wedgewood made 40 saves for the Coyotes (19-36-4), who have won five of their past six.
"That was not a Picasso, but they do not have to be Picassos all the time," Arizona coach Andre Tourigny said. "I think the 'Sens' played really well. They play heavy, they hit, they were strong on pucks. We had no answer for two periods, but [Crouse] decided we'll have a game."
Josh Norris scored twice, and Brady Tkachuk had two assists for the Senators (21-33-5), who also lost 8-5 to the Coyotes on March 5. Filip Gustavsson made 10 saves and has lost his past seven games.
"I don't think we've had the puck that much and dominated a game for that long maybe since I've been here," Ottawa coach D.J. Smith said. "I can't think of the last time. [The Coyotes] could barely get to the red line at one point. We just didn't score. You have to score."
Norris gave Ottawa a 1-0 lead at 2:39 of the first period. He scored on a rebound near the left post after Wedgewood stopped Tkachuk with the toe of his pad while sliding across the crease.
Crouse tied it 1-1 at 7:49, taking a pass from Phil Kessel on a 2-on-1 and scoring with a wrist shot glove side from the slot. He then made it 2-1 at 9:00 with a deflection of Shayne Gostisbehere's point shot on the power play.
Norris tied it 2-2 with his own power-play goal at 14:01, beating Wedgewood from the top of the right circle after the puck popped out to him on a face-off. He has scored six goals in his past six games.
"He's scoring, he's playing, he's checking. He did everything we asked him to do tonight," Smith said.