Mrazek, who made his first start since Jan. 1, won for the first time since Dec. 3.
"It felt good to get the win for us, especially after two wins, that's nice," Mrazek said. "Keep rolling so that ... we learn how to win games."
Sam Lafferty, Andreas Athanasiou and Taylor Raddysh scored for the Blackhawks (11-25-4), who are on their longest winning streak since a four-game run from Oct. 15-25.
Raddysh gave Chicago a 3-2 lead at 6:36 of the third period. Jonathan Toews sent a cross-ice pass to Tyler Johnson in the left face-off circle, and he sent it across the crease to Raddysh for a tap-in.
"Yeah, I think three complete games, and even a couple of games before that, I think I mentioned before, I thought we were coming," Chicago coach Luke Richardson said. "We had 40, 45 minutes, 50 minutes where we, not ran out of gas, but a team with maybe a little more depth flexed their muscles on us. We were right there, and I think just to see some results for the guys, and now that they see it, I think they're pushing harder. I've been talking about us being connected on the ice, but off the ice, you can feel it."