Algeria started brightly as Houssem Aouar found space early, but his rushed shot from inside the box went wide.
And just like that, Switzerland pounced. On the ten-minute mark, a superb run from Johan Manzambi took the highly-rated star into the box before turning the ball inside for a patient Breel Embolo to tap home from close range and net his second goal of the campaign.
For much of the remainder of the half, both teams struggled to ceate clear cut chances. That was until the dying embers when Algeria fluffed their best chance of the match. Ibrahim Maza’s inaccurate effort left the North Africans visibly disappointed.
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Switzerland scored inside the very first minute of the second stanza to rub salt in the wound. The Algerians failed to clear the ball and that presented Dan Ndoye with the chance from 15 yards out, which he fully capitalised on to double their lead.
Fabian Rieder had a chance to put the game well and truly to bed in the 80th minute, but he would inexplicably miss a wide-open goal with a side-footed effort that went awry.
Switzerland – who are now unbeaten in their last seven games – will face Colombia or Ghana in the last 16 on Tuesday.