Grundstrom got the second deflection on Drew Doughty's shot to give Los Angeles the lead at 13:55.
"We weren't ready to back down," Kings defenseman Kale Clague said. "I'm really happy for everyone to get back on the winning track, and I know we all just want to carry that over into the weekend."
Clague, Doughty and Trevor Moore each had two assists, and Jonathan Quick made 24 saves for the Kings (15-17-6), who had lost three straight.
Lawson Crouse had a goal and an assist, and Jakob Chychrun had two assists for his third straight multipoint game for the Coyotes (19-16-5), who lost for the first time in four games.
Adin Hill made 26 saves and is 6-2-0 in his past eight starts with Antti Raanta and Darcy Kuemper each out because of a lower-body injury.
"We needed some more from some guys, really key guys," Arizona coach Rick Tocchet said. "It was 3-1, and they shot a couple of pucks and took them in, and we didn't box out. It's unfortunate. That's a game you've got to win."
Adrian Kempe got the Kings within 3-2 at 1:18 of the third, scoring on a give-and-go with Clague during an odd-man rush six seconds after killing a penalty.
"We did a great job on the kill and [Kempe's] goal got us going a little bit, and we just played on our toes throughout the third," Clague said. "A lot of good O-zone time and we just kept pushing and we got our bounces."