Clayton Keller had two goals and an assist, and Oliver Ekman-Larsson had three assists for Arizona (21-13-4), which is 2-1-0 since acquiring Hall in a trade from the New Jersey Devils on Dec. 16.
Hall has three points in the three games, and the forward's impact has been felt throughout the Coyotes lineup. His arrival allowed coach Rick Tocchet to juggle his top scoring lines, putting Keller and Nick Schmaltz together with center Carl Soderberg.
[WATCH: All Red Wings vs. Coyotes highlights]
Against Detroit, that line scored the first three goals of the game, playing most of its shifts with the defense pair of Ekman-Larsson and Jordan Gross, who made his NHL debut.
"The Soderberg line was really good out there," Tocchet said. "They had good puck possession. [Keller] was feeling it tonight. … He's having fun out there and he's doing the right things. … It seems like when he plays good defense, the other parts of his game are really good."
Video: ARI@DET: Keller beats Howard with sizzling wrist shot
Ekman-Larsson said, "It's easy to play with those guys right now. They've built some chemistry in these last three games, and we're just trying to get them the puck when they get open."
The Red Wings (9-26-3) have lost four games in a row and 16 of 18 (2-14-2) going into the Christmas break.
"I thought we played pretty well until they scored, but we're letting goals weigh us down," coach Jeff Blashill said. "We've got to have a short memory; it was 1-0, not 10-0."
Antti Raanta made 28 saves for Arizona in his first start since No. 1 goalie Darcy Kuemper was injured in an 8-5 loss at the Minnesota Wild on Thursday. Kuemper is week to week with a lower-body injury.
"I thought he was really good out there," Tocchet said. "You could tell he was ready to get out there and play."
Jimmy Howard made 40 saves in his return after missing 10 games with a lower-body injury for Detroit.
Video: ARI@DET: Howard snares Oesterle's golden opportunity
"Physically, I felt fine and I had fun being back out there," he said. "They were just quicker to pucks and quicker in every aspect."
The Coyotes took a 1-0 lead at 13:25 of the first period when Keller scored with a one-timer off a Schmaltz pass.
Keller scored his second of the game at 16:43 to put Arizona up 2-0, beating Howard with a wrist shot from the top of the right face-off circle, again off a pass from Schmaltz, who has six assists in the past three games.
"I think we play the game a lot like each other, so we can feed off each other really well," said Keller, who has five points (three goals, two assists) in the past three games. "[Soderberg] is huge in front of the net, which creates space and makes it easy to work."
The Coyotes went ahead 3-0 39 seconds into the second period when Howard deflected Soderberg's shot into his own net.
Video: ARI@DET: Soderberg capitalizes on Howard's error
Hall, who is playing with Phil Kessel on a line with center Christian Dvorak, gave Arizona a 4-0 lead at 5:41 of the third when he beat Howard with a high wrist shot from the right face-off dot.
Filip Zadina scored unassisted at 9:59, three seconds after a Coyotes penalty ended, to get the Red Wings within 4-1, but Dvorak redirected Ekman-Larsson's shot past Howard to make it 5-1 at 10:26.
Tyler Bertuzzi scored his Detroit-leading 14th goal to make it 5-2 at 15:31.
"We obviously wanted to have a big game after [the loss to the Wild]," Ekman-Larsson said. "We've been pretty good on the road all year, so we felt like we were going to bounce back and have a good game."
Video: ARI@DET: Bertuzzi weaves a wrister through Raanta
They said it
"I was pretty nervous for the first couple shifts, but [Oliver Ekman-Larsson] did a great job of talking me though each situation, and after that it was great. I just tried to keep things simple, keep the pucks going north and not make any mistakes." -- Coyotes defenseman Jordan Gross, who was plus-3 with an assist in his first NHL game
"We were a step behind all night, and that's been something that has happened in a lot of games this season. I guess Christmas comes at a good time this year, so we can step away, spend some time with the family, and forget about all this. Things have to change when we get back from this little break." -- Red Wings forward Frans Nielsen
Need to know
Dvorak's goal was his 100th NHL point. Gross got his first NHL point with an assist on it. ... Keller became the first player in Coyotes history to have four games with at least three points before turning 22 years old. ... Soderberg has two goals and an assist in the past three games. ... The Red Wings placed forward Anthony Mantha (upper body) on injured reserve before the game and activated Howard.
Coyotes: At the Nashville Predators on Monday (8 p.m. ET; FS-TN, FS-A PLUS, NHL.TV)
Red Wings: At the Florida Panthers on Saturday (7 p.m. ET; FS-F, FS-D+, NHL.TV)
Video: Keller has three points, Hall pots first goal in win