Chicago trails the Vancouver Canucks and Winnipeg Jets by six points in the Western Conference wild-card race.
"Important win for us," Blackhawks coach Jeremy Colliton said. "First game after that road trip and typically that's a tougher one, but I was pretty happy with our start, first 10 minutes, I thought we were aggressive and did a lot of good things. The second 10, didn't love as much. I thought we turned the puck over and gave them some free chances.
"But then I thought we won the game in the second period; when we came out, our first couple of rotations were excellent, then we score the goal. I thought that's where we won the game, so that's something we've been talking about is trying to string multiple shifts together to build momentum and we did that and big win."
Corey Crawford made 37 saves in his sixth straight start. Malcolm Subban did not make a save in 1:10 in the third when he entered the game for Crawford after Ryan Getzlaf's left knee hit Crawford in the head and he was pulled by a concussion spotter. It was Subban's first game with the Blackhawks since being traded from the Vegas Golden Knights on Feb. 24.
Danton Heinen scored for Anaheim (26-32-8), which is 2-5-1 in its past eight games. John Gibson allowed five goals on 24 shots in the first two periods, and Ryan Miller made 15 saves on 16 shots in the third.
"[Miller was] good," Eakins said. "That's always a tough spot, right? Sitting on the bench or back in the dressing room and then to be called in like that it's tough. He's such an unbelievable pro and such great experience, and I thought he stepped up for us."
Drake Caggiula skated to the front of the net and tapped in Boqvist's shot past Gibson's right skate to give the Blackhawks a 1-0 lead at 2:07.