Bernier made 48 saves and Smith scored at 4:18 of overtime and Toronto beat the Dallas Stars 3-2 on Thursday.
The Leafs won for the first time since Nov. 23.
"I'm happy we won because there seems to be a lot of pressure on our group, and hopefully this helps flush some of the things that are going on out there that we can feel a little bit of room to breathe what we went through," coach Randy Carlyle said.
"By no means that we think we're out of the woods, but it feels good to win a hockey game."
For the 10th consecutive game, the Leafs were outshot. Bernier called being outshot -- this time 44-22 in regulation and 50-24 total -- this team's "style."
"My job is to go out there and give my team a chance to win," Bernier said. "I thought my last couple of games, I wasn't very good. I needed to come here and play the way I can play and go shot-by-shot."
Bernier's performance didn't surprise Carlyle or his teammates.
"I'm not that impressed anymore because he's done this night in and night out," said center Nazem Kadri, who scored twice.
"It's almost expected of him now. He's been a great contributor to this team even throughout those tough stretches when they had us pinned in our end. Our goalie needs to make a couple big saves for us to get the win, and that's exactly what happened."
Bernier earned praise from Stars coach Lindy Ruff.
"I give their goalie a lot of credit. I give their team a lot of credit. They found a way to win," Ruff said.
Bernier wasn't perfect. Erik Cole beat him with a goal on the rush early in the third period when the Leafs got caught on a bad line change, and then Shawn Horcoff tipped a shot in on the power play to tie the score at 17:14 of the third.
Horcoff almost had a similar goal at the 9:42 mark of the third when he redirected a power-play point shot past Bernier. But the referees waved it off right away and video review upheld the no-goal call.
"I was hoping they'd count it, but I felt like it was a little bit high," Horcoff said. "I knew the next one was OK."
When Kadri scored his two goals, there was no doubt. His first came because of some sharp passing from linemates Phil Kessel and James van Riemsdyk 58 seconds into the second period.
Kadri added another, his ninth of the season, 6:58 into the third. He didn't grab that puck but did call Thursday night a "memory" because the game was dedicated to his grandfather, who died earlier this week.
"It's definitely something that he would've loved to see," Kadri said. "In the last couple years there hasn't been a game he's missed. He's going to be dearly missed by our family."
Kadri returned after missing Tuesday night's loss to the San Jose Sharks to attend his grandfather's funeral in London, Ontario.
When he came back, he was on the first line between van Riemsdyk and Kessel because Tyler Bozak is out indefinitely with an oblique strain.
Another player who has made the most of his opportunity is Smith, who scored his fourth goal of the season.
On a team that's lacking in secondary scoring and has grown accustomed to being outshot, Smith put two on net in regulation and then scored the winner.
"Overtime, that's a lot of fun," Smith said. "Real exciting looking up at the crowd after scoring."
Horcoff scored with four seconds left on that penalty. It was the ninth power-play goal Toronto had given up in its past six games.
"It's a big part of when you're struggling and things not going your way as far as handling pucks and pressure," Carlyle said. "We were four seconds away, but we still had two chances to clear the puck. It would have been over. But that little bit of adversity hurt us for a period of time."
The Leafs were happy to break the skid.
"We had to break it," Smith said. "We haven't been playing well, and I don't think we put together 60 minutes at all tonight. But with Bernier playing over his head for us and giving us a chance to win, that's all we can ask for."
Led by Bernier, Smith and Kadri, the Leafs go to Ottawa for Saturday night's rivalry game against the Senators unburdened by the pressure of this skid.
"Hopefully they feel good in there and we can flush what's been going on because there's been a lot of things going on," Carlyle said. "And we just think that it's time for this group to take a deep breath and let's go to work tomorrow and get ourselves ready for Saturday."
The Leafs held a pregame moment of silence to honor Nelson Mandela. His name along with his dates of birth and death were put on the scoreboard along with a profile photo of the South African leader. ... Winger Jerry D'Amigo, called up earlier in the day as the Leafs placed Bozak and enforcer Colton Orr on injured reserve and Jerred Smithson cleared waivers, made his NHL debut playing on the fourth line and finished with 4:02 of ice time. Stars defenseman Trevor Daley left the game with a lower-body injury after getting tangled up with van Riemsdyk on the play that led to Kadri's first goal. Daley's left leg got caught up with the Leafs winger, and he slid into the boards. ... Defenseman Morgan Rielly was a healthy scratch for the Leafs as Cody Franson returned after missing three games with a lower-body injury.