The hosts, playing in its first Olympics, will now play favourite Brazil at Wembley Stadium on Tuesday to decide which team wins Group E.
Captain Casey Stoney opened the scoring in the 18th minute, tapping in from close range after Cameroon failed to clear a free kick. Jill Scott doubled the lead four minutes later when she sidefooted in a backheel from Kim Little that cut through the Cameroon defence.
Britain continued to look dangerous, and could have scored three more by the time it left the pitch at halftime to a standing ovation.
Stephanie Houghton scored her second goal of the tournament late in the game as Britain exploited gaps left when Cameroon was pressing for a goal.
Little passed back to her on the edge of the area, and she shot powerfully to the right of the keeper, capping a solid team performance that will add to expectations the team could be a medal contender.
"I thought the girls were very disciplined and the strategy worked. We won the game and are into the quarterfinals," said Britain coach Hope Powell,
She said the team was now focused on Brazil.
"We will be looking to win, it's at Wembley," she said. "It will be a fantastic occasion."
Cameroon, which lost 5-0 to Brazil in its first game, will face New Zealand for third place in the group.
The top two teams from each of the three groups automatically advance, along with the best two third-place finishers.
Cameroon's best moment came in first-half stoppage time when Francine Zouga flashed a long-range shot just wide.