Embolo, born in Yaounde but raised in Basel, struck three minutes after the restart from a Xherdan Shaqiri cut-back to put them top of the section.
The 25-year-old refused to celebrate the goal as the small group of Swiss fans cheered wildly at Al Janoub Stadium.
The goal came after Cameroon, without a win in the World Cup for 20 years, had dominated the first half, missing several good chances to take the lead.
The Indomitable Lions, who eliminated Algeria in a playoff to qualify for the tournament, had outplayed the Swiss in the first 45 minutes with quick combinations, speed and power as their opponents remained toothless up front.
The Swiss were in trouble again a little later with in-form forward Eric Maxim Choupo-Moting snatching the ball from an opponent to charge into the box only for Sommer to block his effort.
In search of their first win at a World Cup in 20 years, Cameroon were bolder, taking on their opponents in one-on-one situations, while the Swiss rarely managed to get into their opponents' box.
Switzerland, who reached the round of 16 in the two previous World Cups, struck at the start of the second half with Xherdan Shaqiri cutting into the box and Embolo tapping in what proved to be the winner.