Palmieri has at least one point in four consecutive games and has two goals in two of the four games. He leads the Devils with 29 goals and 52 points.
"It'd be nice [to score 30 goals this season]," Palmieri said. "Obviously, there are a couple games left here, and right now, I think our group is just having a lot of fun trying to string some wins together in a playoff race here. I think some people count us out, but we haven't been eliminated yet, so we just want to keep going."
Adam Henrique scored his 27th of the season, 9:57 into the third period.
Crosby's 12-game scoring streak (six goals, 20 points), which was the NHL's longest active streak, ended; he failed to score for the first time since Feb. 27.
"We didn't play well enough here," Crosby said. "That's what we have to focus on, is making sure we're better. … We were well rested. We understand how important the games are at this point, but we didn't play well enough. So, we didn't deserve to win that one."