The Rennes frontman set up both Ruben Vargas and Johan Manzambi after the break as the Swiss ensured they will return to the same venue in the knockout stage despite substitute Promise David's reply.
Jesse Marsch's side, who finished above Bosnia and Herzegovina by virtue of their head-to-head record, face a trip to Los Angeles.
"We're going to go to LA, we're going to go where it's probably going to be an away crowd and it will be a little bit tougher, but we still want to electrify our country and play really well down there and go after it still," the American told ITV.
"We're exactly where we want to be. We finished second in the group, we're in the knockout phase and now let's go for it."
The Swiss should have been ahead within 11 minutes on Wednesday (Thursday AEST) when Embolo was played in behind defender Richie Laryea, only to see his shot blocked by keeper Maxime Crepeau before Manzambi's follow-up was repelled by Derek Cornelius.
Canada frontman Cyle Larin was equally wasteful two minutes later, although an offside flag belatedly spared his blushes, but he did significantly better after running on to Jonathan David's 33rd-minute pass, forcing a solid save from Gregor Kobel with a curling right-foot attempt.
Kobel clawed away Ali Ahmed's strike at his near post after he had been picked out by Jonathan David, who later lashed a left-foot shot wide, with four minutes of what proved to be a goalless first half remaining.
However, the game exploded into life within 40 seconds of the restart when Embolo smuggled the ball away from full-back Alistair Johnston on the Swiss right and crossed to the far post, where Vargas blasted past Crepeau at his near post.
The Canada keeper was culpable as Murat Yakin's men extended their lead with 57 minutes gone, allowing Manzambi's shot to squirm from his grasp after Embolo had held the ball up and laid it into his run.
Promise David gave his side hope with 14 minutes remaining when he dispatched Nathan Saliba's fine cross emphatically past Kobel, but Johnston was unable to direct his header past the keeper deep into added time.
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