Smith tied the game 1-1 at 2:30 of the second period when he scored on a breakaway off a turnover.
"We deserved better tonight and it's one of those things where we play again in a couple of days and just have to have a short memory and grow from it, learn from it and move on," said Rangers defenseman Marc Staal, who returned after missing 13 games with an ankle injury.
Price won his 333rd NHL game, tying him with Nikolai Khabibulin and Gump Worsley for 24th on the NHL list. Price was 1-5-1 with a 4.44 goals-against average and .849 save percentage in his prior seven starts, allowing at least five goals in four of them.
"He's a big leader for us and he's been working so hard for so many years," Danault said. "Obviously we want to play better for him. He saved our [butts] a lot of times and he was big for us tonight."
The Canadiens blew a 4-0 lead in a 6-5 loss to the Rangers on Nov. 23.
"I'm kind of at the stage now where I'm pretty good at letting those types of things go and just focusing on today," Price said. "I don't think either team was happy with the goals against the last round. So back-to-back games, guys were definitely being on the more safe side of things tonight."