Benn cut it to 2-1 at 2:18 of the third, kicking the puck following Tyler Seguin's redirection to his backhand and scoring into an open net in front.
Alexander Radulov tied it 2-2 at 10:46 on a one-timer short side from the left circle after receiving a drop pass by Andrej Sekera from behind the net.
"It's not an easy game, it's a battle game, a hard game," Khudobin said. "We found a way, we got a huge two points, and we found a huge team effort."
Hintz gave Dallas a 3-2 lead at 15:51. Denis Gurianov attempted to throw the puck to the net from a sharp angle along the right boards, but his shot deflected off the stick of Richardson to Hintz, who scored into an open net.
"There were three plays (by) three individuals and blown coverages," Coyotes coach Rick Tocchet said. "We leave [Benn] in front. Radulov, you've got to protect the house on that play. And the third goes back door, you're just sleeping. Three plays."
Mattias Janmark, who left the game briefly in the first period following a hit by Taylor Hall, scored an empty-net goal at 18:24 for the 4-2 final.
Hall scored his second goal in six games since being acquired in a trade with the New Jersey Devils on Dec. 16 to give Arizona a 1-0 lead at 8:42 of the first.
Garland, who was promoted to Hall's line after a 4-1 loss to the Vegas Golden Knights on Saturday, extended the lead to 2-0 at 18:02 with a sharp angle shot off the pads of Khudobin.
"There was some talk (in the room) after that, we got outshot pretty bad (22-5 in the first period) and a 2-0 lead by them," Benn said. "We needed a kick in the butt, and we found a way to come back and get two points."
Coyotes forward Derek Stepan (concussion protocol) left the game at 2:43 of the second period following a hit behind the net by Stars defenseman Jamie Oleksiak, who was assessed an interference penalty on the play.
Dallas' next game is the 2020 Bridgestone NHL Winter Classic against the Nashville Predators at Cotton Bowl Stadium on Jan. 1.
"We've got two days to get ready for it and kind of take it in and enjoy it," Benn said. "But at the same time, it'll be big points on the line against a division rival."