Subban scored 23 seconds into overtime and Price stopped 40 of 44 shots to give Montreal a wild 5-4 victory against the Ottawa Senators on Thursday.
Subban beat Craig Anderson on the only shot in overtime in a game that saw the Canadiens jump out to a 3-0 lead in the first period, only to give up four unanswered goals while being outshot 38-17 in the first two periods.
"Well, it was big, obviously," Price said. "We were in a situation to win a hockey game and it really felt good to get that one capped off."
Price made a number of sensational saves in the second to protect Montreal's 3-2 lead before he was beaten on Ottawa's final two shots of the period.
"Listen, I know he's my teammate and everything, but I'm hard-pressed to find another goalie that's better than him right now in the world," Subban said. " ... Just watch the tape. It's pretty incredible."
The Canadiens recovered in the third, and Tomas Plekanec tied it 4-4 when he got credit for his second goal of the game with 8:58 remaining.
"I don't think there was much needed to be said," Price said. "We've got a lot of leadership in this room, a lot of experience, and everybody in this room realized that our effort wasn't quite good enough, and we took it upon ourselves to make it right and we took advantage of our opportunities."
Plekanec, who opened the scoring with a shorthanded goal at 2:04 of the first period, drove in on a breakaway and was stopped by Anderson, but the rebound went into the net off the skate of Ottawa defenseman Jared Cowen.
"It was Carey Price's game," Plekanec said. "It definitely feels good. He deserves that, but we didn't as a team in front of him."
Erik Karlsson had a goal and two assists, and Clarke MacArthur had a goal and an assist for the Senators, who defeated the Canadiens in the first round of the 2013 Stanley Cup Playoffs and won the first two games between the teams this season.
Ottawa coach Paul MacLean was not about to lay the blame on Anderson, who made 18 saves.
"It's overtime," MacLean said. "We weren't very good at the start. We gave up a shorthanded breakaway right at the start of the game; that's a tough spot to put him in. Would we like to see the save? Oh yeah, we'd like to see the save, but it's a breakaway from the blue line in. But at the end of the day I thought he made some saves to give us a chance to get the game tied up and get the lead, and the team wins, and the team loses."
Price, who will represent Canada at the 2014 Sochi Olympics, made a spectacular glove save on Milan Michalek's shot from the slot, the Senators' 30th of the game, at 9:06 of the second period. Price stuck out his left pad to steal a sure goal from Ryan later in the period before making another glove grab to deny Mark Stone at 15:02.
"He was the difference, right?" Ryan said of Price. "That game could have been a much different game going into the third if it wasn't for him. He made three, four, maybe five 10-bellers right in a row."
Ryan broke through to tie it 3-3 with his team-leading 19th goal at 17:16. Turris gave the Senators their first lead at 18:40 when he took a return pass from MacArthur and beat Price with a backhand for his 14th goal.
"This is one of those games that brings out a huge range of emotions," Ryan said. "You get down when you think you're dominating for the most part, then you come back and show that resiliency to compete for that point in overtime, and then you blow a lead and you lose and you don't get to the shootout.
"For me, the way I look at the game as a team, I think we've got to take a lot of positives because we showed fight that we didn't show fight earlier in the year, so that's what I'm going to take out of it."
Plekanec, who will captain the Czech Republic at the Olympics, fell to the ice after he was struck on the right leg by a shot by Ottawa's Cory Conacher midway through the first period. Plekanec went to the dressing room briefly before returning.
Max Pacioretty made it 2-0 for Montreal with his team-leading 21st goal on a power play at 14:05. David Desharnais, who missed the Canadiens' 4-1 loss to the New Jersey Devils on Tuesday because of the flu, scored at 15:36 to increase Montreal's lead to three.
Ottawa scored two goals 1:12 apart late in the first to draw to within 3-2. MacArthur scored his 17th goal at 17:13. Karlsson was left unmarked to score into a wide-open net at 18:25, his 11th.