The Portuguese leader of the Movistar team kept his head down and his legs pumping long enough to win the gruelling 205.7-kilometre event by a nose over Frenchman Pierrick Fedrigo in a thrilling finish to the five hour 20 minutes 18 seconds race.
Da Costa, Fedrigo and Stefan Denifl of Austria broke away on the last of the 17 laps up and down Mount Royal near downtown, but their lead looked to be slipping away with each stroke of the pedals as some of the world's top riders led a desperate peloton into the final sprint.
Philippe Gilbert, the world's top-ranked rider, caught the flagging Denifl for third place, but couldn't touch the other leaders.
"We came down to the last climb with a 50 seconds lead, so we were pretty confident," Da Costa said through a translator. "We never looked back.
"This is the result of good work by the team. We did our homework for this race. We didn't want to come back from Canada empty-handed, so it paid off."
Gilbert, the winner of another one-day "classic" race on Friday in Quebec City, finished two seconds back along with his Belgian compatriot and Omega Pharma teammate Jurgen Roelandts and Denifl.
Victoria's Ryder Hesjedal was marking Gilbert, defending champion Robert Gesink and American Levi Leipheimer at the front of the charging peloton and came in 11th.
Hesjedal, who made his breakthrough with a seventh place finish at the Tour de France in 2010, was third at the inaugural Montreal race last year after finishing fourth in Quebec City. He had been 18th in Quebec this time.
"I can't say I'm disappointed because to race here in Canada is a very important part of the season for me," he said. "Certainly, with my results last year, you could look at it as not doing as well, but every season is different.
"The level here was very good. The team rode well both events. We were right there today. That's the way racing goes."
Gilbert took the world No. 1 ranking from Tour de France winner Cadel Evans with his win in Quebec City and added another 50 points by finishing third. His 698 total is 124 points better than Evans, who opted out of the Canadian races. Two events remain on the 27-race WorldTour season.
It had been a tough day for the 29-year-old, who had a puncture on the fourth lap, then was knocked over when Dominique Rollin of Boucherville, Que., crashed on the fifth lap.
Gilbert rejoined the peloton, but Rollin abandoned with bumps and bruises and a cut lip. He hit a hole in the road and the bike skidded out from underneath him. He said he was not aware that it was Gilbert who went down with him.
"This is a great result after that crash," said Gilbert, clearly a favourite among the thousands of spectators lining the route on a near perfect sunny day for racing. "When I crashed I was really scared.
"I thought maybe it was over for the world championships (in Denmark in two weeks). It was like last year when I crashed at the Vuelta (Tour of Spain) when I was wearing the leader's jersey."
Gilbert is a star rider in Europe. His 16 wins this year include becoming only the second ever to sweep the three Ardennes Classic races in April, but he was surprised to see his popularity extended to North America.
On the podium, he asked for the microphone to say thanks to a cheering throng of fans.
"I had no idea I had so many fans in Canada," he said. "It's good for our sport that our fans are not only in Europe."
It was also a big day for Fedrigo, who is on the rebound from battling Lyme Disease, which took weeks for doctors even to diagnose and caused him to miss the Tour de France.
"It really wipes you out," he said. "But I got it cured and I'm getting better and better. I want to finish the year on a god note and start fresh in 2012."
David Veilleux of Cap Rouge, Que. led a promising breakaway attempt with four laps to go. While he was caught, the Europcar rider came in with the peloton in 22nd place.
Veteran Michael Barry of Toronto was 54th, Francois Parisien of Repentigny, Que., was 62nd, Svein Tuft of Langley, B.C. was 66th and Ryan Roth of Cambridge, Ont., was 108th.
Of the 173 who started, 112 finished. Gesink, who was second in Quebec City, finished 36th.
It was the last race of the year for Hesjedal, who opted to skip the world championship where he felt he would have little chance to win the road race.
"The course is more suited to sprinters," he said. "Anything can happen, but to go back over to Europe and try to perform on a course like that, well, we'll see what happens, but if it ends in a big bunch sprint then it will definitely have been the right decision.
"I end my season here healthy and feeling strong. I'll start next year even earlier than this year at the Your Down Under (in January)."