Johan Franzen tied it for Detroit on a power-play breakaway 42 seconds into the third period, and Hudler sent a low slap shot past Roberto Luongo's blocker on the first shootout attempt.
Howard, who made 34 saves through overtime, stopped Jeff Tambellini, Ryan Kesler and Daniel Sedin in the shootout for the Red Wings. Detroit snapped the Canucks' eight-game winning streak.
Howard started for the second straight night for the injury-riddled Red Wings, who lost top-pair defenseman Brad Stuart to a broken jaw Friday in Calgary.
Osgood was scheduled to start in goal, but a nagging groin injury forced Howard to play again.
"I just found out after the pre-game skate that I was going to be playing here tonight," Howard said. "I knew coming to the arena this morning that it was iffy with Chris with his groin. I feel bad for him. He wants to be out there. He's such a great competitor. He loves battling out there for the guys."
Despite the loss, Vancouver remained atop the NHL standings with 60 points, one more than Detroit and three ahead of Eastern Conference-leading Philadelphia.
Daniel Sedin scored a second-period, power-play goal, and Luongo made 32 saves for the Canucks, who haven't lost in regulation in 16 games (13-0-3) -- dating to Dec. 5. Vancouver is 17-1-3 in its last 21 games, but two of the losses come against the Red Wings -- including a 5-4 overtime decision in Detroit on Dec. 22.
"It was a fun game to be a part of so I just would have let the boys play and settle it out old-school style," Luongo said. "But you know, shootouts sometimes you win, sometimes you lose."
Things were a lot tighter Saturday between the League's top two offensive teams, perhaps because both clubs played Friday.
Tambellini shot wide after the puck rolled off his backhand attempt on a breakaway with two minutes left in overtime, and Detroit's Niklas Kronwall had a goal waved off with 24.5 seconds left because Todd Bertuzzi bowled over Luongo.
Henrik Sedin's 180-foot pass bounced off the end boards to twin brother Daniel, who was streaking in alone behind the Detroit defense. His quick deke to the backhand left Howard on his backside, but the goalie reached back with his glove and picked the shot out of the air over the goal line. Video replay confirmed that a goal wasn't scored.
"It was a playoff type of game," Tambellini said.
Howard made two more great saves on Daniel Sedin in the first period, and got a break when Keith Ballard hit a post six minutes into the second. Daniel scored his 25th goal into an empty net with 7:51 left in the second after Henrik Sedin's shot from the right circle caromed to the other side.
Franzen tied it on the first shift of the third.
"Our guys really battled hard," Wings coach Mike Babcock said. "We got really good goaltending from our goaltender. We both have real good teams, real deep teams. I thought we just hung in there and battled."
Material from wire services and team media was used in this report.
1 - 0 VAN