Jonathan Bernier made 37 saves for the Red Wings (4-10-1), who are 1-9-1 in their past 11 games. They have been outscored 28-8 while losing their past six road games.
Detroit was shut out for the second time this season; the Red Wings lost 2-0 at home to the Buffalo Sabres on Oct. 25.
"Some of our high-skill players didn't compete hard enough tonight," Red Wings coach Jeff Blashill said. "We didn't have enough of our A-game players tonight. A lot of young guys weren't good enough tonight."
Connolly gave Florida a 1-0 lead at 3:05 of the first period, three seconds after the end of a power play. He scored with a wrist shot from the left face-off circle.
Barkov made it 2-0 at 16:54 with a power-play goal on a rebound after Bernier stopped Huberdeau's wrist shot.
Huberdeau made it 3-0 at 6:45 of the second period when his shot went off Detroit defenseman Trevor Daley's skate. Defenseman Anton Stralman got his 200th NHL assist on the play.
Huberdeau scored again at 10:46 of the third period when he went to the left post and redirected Yandle's pass from the slot into a wide-open net.
It was Huberdeau's 18th two-goal game in the NHL, his third this season and his second in two games. He came close to getting his first NHL hat trick later in the third period, but Bernier made a pad save on his redirection.
"Obviously, I was looking to shoot a little bit more," Huberdeau said. "Obviously, I want my first hat trick at some point. I think [someone] was saying, like, 18 games with two goals. That's too many. Hopefully, it's going to come, but I'm just happy that we got the win."
Bobrovsky didn't face more than eight shots in any period of his 34th NHL shutout.
"Very happy for him," Barkov said. "He's been unreal for us this season and finally gets the shutout and a lot of confidence from that. We're a confident group right now. We're going to keep working hard and keep playing hard."
