Crosby and Kris Letang scored 16 seconds apart late regulation to tie the score for Pittsburgh after Vancouver grabbed a 4-2 lead.
Marc-Andre Fleury made 22 saves for the win.
Chris Higgins, Zack Kassian and Christopher Tanev each had a goal and an assist, while Jason Garrison also scored for Vancouver (23-14-8). Eddie Lack made 31 saves as the Canucks lost their fifth game in a row.
Tied 2-2 in the third, Vancouver looked to be on its way to a victory when Higgins beat Fleury through the five-hole on a breakaway with 6:53 left in regulation and Kassian batted a puck down off the rush and swatted it past the Penguins goalie at 6:36.
But Letang scored with 1:11 left in regulation with Fleury on the bench and Crosby tied it 16 seconds later.
Lack was called upon to make a couple big saves in overtime, including one off of James Neal on a 2-on-1.
Luongo, who was named to Canada's Olympic team along with Canucks defenceman Dan Hamhuis earlier in the day, had just returned to the lineup after dealing with a groin issue.
Tuesday's game marked the first for Crosby at Rogers Arena since his overtime goal in the gold-medal game at the 2010 Games.
Crosby and Penguins linemate Chris Kunitz were also named to Canada's Olympic team earlier in the day.
Down 2-1 after two periods, Vancouver tied the score at 7:39 of third when Tanev's shot from the point beat Fleury through traffic for his fifth of the season.
Higgins then added his twelfth of the season before Kassian rounded out the scoring with his eighth as the Canucks picked up their first victory of 2014. Between the two goals Lack made a big blocker stop on Neal.
With Pittsburgh leading 1-0 after the first period, Fleury made a breakaway save on Canucks forward Jannik Hansen early in the second. The Penguins broke back the other way with Malkin beating Lack on a shot through traffic from the slot for his 12th of the season at 5:25.
Fleury had a bit of luck a bit later in the period as Canucks defenceman Yannick Weber rang a shot off the post, before Penguins counterpart Letang found iron behind Lack.
Letang had two more great chances to extend the lead, but Lack made a couple of huge saves before Garrison cut the Penguins' advantage in half at 15:35.
After Crosby blindly threw the puck in front of his own net right to Garrison, the Vancouver defenceman ripped a shot by Fleury for his fifth of the season and first in 14 games.
Gibbons opened the scoring at 13:15 of the first period after Hamhuis failed to control the puck at the Pittsburgh blue-line. Playing on a line with Crosby and Kunitz, the undrafted 25-year-old free agent out of Boston College raced in alone and beat Lack through the five-hole for his second goal of the season in just his 11th NHL game.
Pittsburgh's No. 1-ranked power play went to work later in the period, but Vancouver's top-ranked penalty kill weathered the storm.
Things nearly got worse for Hamhuis, who will be making his Olympic debut next month after playing seven times for Canada at other international tournaments, in the final minute when Malkin jumped on his turnover and nearly beat Lack from in close.
Notes: Fleury was Canada's No. 3 goalie at the 2010 Olympics in Vancouver, but didn't make the squad announced earlier Tuesday. ... Crosby was still recovering from his concussion issues when the Penguins made their last visit to Vancouver at the start of the 2011-12 season. ... Canada's goalies in Sochi will be Luongo, Carey Price and Mike Smith. ... A total of seven Canucks will be heading to the Olympics. Daniel and Henrik Sedin, along with Alexander Edler, will suit up for Sweden, while Ryan Kesler (U.S.), Weber (Switzerland) and Hansen (Denmark) will also take part in the tournament in Sochi. ... On the Penguins' side, Malkin (Russia), Jussi Jokinen and Olli Maatta (Finland), and Brooks Orpik and Paul Martin (U.S.) will compete for their countries. ... The Canucks recalled Joacim Eriksson from the American Hockey League to serve as Lack's backup with Luongo on the shelf. ... Garrison's goal was his 100th NHL point.