After a cautious scoreless first half in which Breel Embolo had the best chance — denied from a one-on-one — the game accelerated immediately after the restart. Rubén Vargas fired Switzerland into the lead just 39 seconds after the interval. Johan Manzambi doubled the advantage in the 57th minute, capitalising on a defensive error and a lapse from goalkeeper Maxime Crépeau.
Canada regrouped quickly. Substitute Promise David arrived from the bench to score a superb volley in the 76th minute, sparking a frantic closing period in which Jesse Marsch's side dominated possession and created repeated chances — Alistair Johnston and Derek Cornelius both coming agonisingly close — without finding the equaliser that would have kept them at home.
Switzerland advance as group winners, qualifying for the last 32 for a fourth consecutive major tournament. Canada, who made history by reaching the knockout stage for the first time, travel to Los Angeles to face the Group A runners-up. Canada finished with 13 shots to Switzerland's six, and an expected goals total of 1.34 against 1.06 for the Swiss.
Switzerland goalkeeper Gregor Kobel said the team was building in the right direction.
"It feels very good; it was our goal to win the group and we did that, so it's a very nice feeling. I think the team is building nicely into the tournament and that's a natural process you're going to have.
"I know that we have conceded late goals but I think it was just how the games were going. We spent a lot of energy and the last two games we were in front, so obviously the opponent tries to do something so more just of a natural process."
Switzerland midfielder Michel Aebischer welcomed the mood in camp while keeping perspective.
"Well, first of all, it's important to go through the group, to the next stage. Then for us, we knew that it was important to finish first, to finish with a win, to get a good feeling, to now rest also a little bit more than if we finished second, so it was an important win today.
"I think we played three good games. The first one with the result not so good, but at the end we got two wins, one draw, so we are confident as a team. We have a lot of players in good shape. We laugh a lot, so we are really confident to play this next game."
Canada goalkeeper Maxime Crépeau acknowledged the disappointment without deflecting from the squad's collective achievement.
"I mean, there is some disappointment on a personal level and collectively because we wanted to top the group. We felt like we had it in us, but the reality of things is that we go to Los Angeles and we will prepare because it's a quick turnaround.
"On the other hand, we've come far. We've come a long way in the programme, and this is the reality of our group now where we're not satisfied with what we have because we always look forward and we always look ahead.
"So the collective feeling, there's a bit of disappointment. We wanted to stay home, but now we have to see against who we're playing, and we're going to go on the road and we know how to play as well in those type of games."
Marsch was entitled to argue a draw would have been fairer on his side given Canada's superior expected goals figure, though Switzerland's goals came at the moments that mattered.