"It wasn't pretty, but they're not always going to be masterpieces," Hall said. "Find a way to make an impact. Find a way to win a game."
WATCH: [All Coyotes vs. Sharks highlights]
Hall, a forward who was acquired in a trade from the New Jersey Devils on Monday, won a puck battle with defenseman Brenden Dillon and backhanded it from behind the net to Oliver Ekman-Larsson for a shot from the left face-off circle that gave Arizona a 3-2 lead at 17:23.
"The win is pretty nice," Ekman-Larsson said. "I think this is why we got Hall. One thing I would say is that he's good at doing a lot of things. He has good speed, a good forecheck, and made a good play under pressure."
Darcy Kuemper made 26 saves for the Coyotes (20-12-4), who won for the second time in four games.
"We got Hall because of that last goal," coach Rick Tocchet said. "He muscled his way through, wins a big 1-on-1 battle, and that is a big play for us."
Tomas Hertl scored two goals for the Sharks (16-18-2), who have lost seven of eight (1-6-1) and two of three since Bob Boughner replaced Peter DeBoer as coach Dec. 11.
"That third goal was going wide, and it hit off someone's leg or knee or whatever," Boughner said. "It was a bad break for us."