The Pole, overwhelming favourite for gold in light of her four French Open titles, was rattled and stunned by a fierce ball to the body early in the third set, but composed herself to earn a 6-1, 2-6, 4-1 victory.
It was not vintage Swiatek by any means but she lived to fight another day as the first Pole to reach the semi-finals at an Olympic tennis tournament.
The clay-court specialist will face China's Zheng Qinwen for a place in the gold-medal match after Zheng outlasted German veteran Angelique Kerber in a three-set thriller.
Swiatek had cruised through the opening three rounds and was in total command after a fast start against eighth seed Collins.
But her game suddenly went off the boil in the second set as Collins became the aggressor from the back of the court.
Things did not start well for Swiatek in the third set when she was off-balance at the net and Collins drilled a groundstroke that caught Swiatek in the midriff - the American walking around the net to check on her opponent.
But it was Collins who began to suffer in the decider and had one visit from the trainer before calling it a day.
