The Australian exploded out of the blocks but had to fend off a late challenge from defending champion Dawn Harper of the US to clock 12.35 seconds.
Harper took the silver in 12.37, a lifetime best, with the bronze going to Kellie Wells, also of the United States, in 12.48.
There was drama after the finish as Pearson and Harper stared at the jumbo screen, neither sure of the result.
Pearson screamed with delight when her result flashed up, while Harper clapped in a show of sportsmanship.
“It’s a dream,” said Pearson, who trained in London for the final few months before the Games.
“Relief was the first thing I felt and then shock. I’m just going through the emotions. I really wanted this. I’ve worked so hard for two years. To see my name on the scoreboard, I just can’t believe it.”
Harper claimed to be happy to win a silver.
“There was so much pressure on me,” she said. “I’m just so happy to be here. I wanted to be here and I wanted to be a part of it.”