Heiskanen cut it to 2-1 at 9:10 on the power play, scoring from the bottom of the left circle off a pass across the slot from Benn.
Shesterkin kept it 2-1 with a highlight-reel, windmill glove save on Wyatt Johnston at 17:26 of the second before he dominated the third.
"We definitely had our chances," Benn said. "I think we're actually playing pretty good. [Monday] night was a great effort. Tonight, probably not for 60 minutes, but we had a chance to win that game. It just didn't happen. We're sticking with the game plan here."
Trocheck scored into the empty net at 18:19 to make it 3-1, but Shesterkin still had to make another four saves to preserve the Rangers' eighth straight victory, their longest streak since winning nine in a row during the 2015-16 season.
"We left January, left the (All-Star) break and came in and said, 'We're turning the page here, this is a new chapter, our actions are the ink, write it down and say what you want to say,'" Laviolette said. "We've just been moving slow with it and the guys have been buying into that."
NOTES: Heiskanen played his 400th NHL game after missing the game Monday because of the birth of his child. … Dallas recalled forward Logan Stankoven from Texas of the American Hockey League before the game, but he was a healthy scratch because Matt Duchene returned after sitting out Monday with a lower-body injury. Stankoven is the AHL's leading scorer with 57 points (24 goals, 33 assists) in 46 games. … The Rangers are 33-2-2 when allowing three goals or fewer this season.