Sustr scored his 2nd goal of the season at 4:37 of the second period to make it 3-0. Kucherov left a drop pass for Sustr, who sent a wrist shot that got past Dubnyk through the five-hole.
"We battled it out," Lightning defenseman Anton Stralman said. "We were down to three lines at the end but we stuck to it and played some good hockey."
Scandella scored at 16:02 of the third period to make it 3-1. Jonas Brodin put a shot on goal and Scandella jammed the puck into the net on the follow up.
"I don't think for the first two periods our puck movement was good enough to get through the neutral zone and make plays," Wild forward Zach Parise said. "When you're fighting for possession you're not going to score a lot of goals."
Kucherov scored his 30th goal of the season into an empty net with 1:09 remaining.
Namestnikov was injured at 3:18 of the second period when his skate got caught under Parise and he needed to be helped off the ice.
Johnson was injured at 8:04 of the second when he was checked by Nino Niederreiter and the two players appeared to bang knees on the boards. Johnson also needed to be helped off the ice.
Paquette went down midway through the third period when he got tangled with Niederreiter and was injured when both players went down to the ice.
"Once [Paquette] goes down we were really in scramble mode," Lightning coach Jon Cooper said. "Give them credit, they were pushing and we bent a little bit but [Vasilevskiy] was there when we needed him."