The five-times champion, who turned 37 last months, tamed the big-hitting Latvian with a rock-solid performance under the Centre Court roof, winning with something to spare.
Ostapenko turned women's tennis upside down when she rocketed out of the pack to claim her first professional title at the French Open last month and the feisty 20-year-old appeared to be gathering momentum on the All England Club lawns.
A rare French Open/Wimbledon double looked within reach for Ostapenko who had struck 121 winners en route to the last eight.
But old maestro Williams, who had already schooled a 21-year-old and two teenagers en route to her 38th grand slam quarter-final, has seen it all before and barely flinched.
There was a wobble when she dropped serve with a double-fault in the second set -- giving Ostapenko renewed belief -- but she never looks ruffled as she reached the semi-finals here for the 10th time in 20 visits.
Making her Centre Court debut Ostapenko was a little more subdued than normal but received a glowing report from the veteran of 75 grand slam campaigns.
"She went for a lot of shots. She competed really well. She kept herself really in the game with her attitude. I thought she just did a lot of things really well and kept it close," Williams, who made her Wimbledon debut in 1997, a few weeks after Ostapenko was born, told reporters.
"I never played her. Didn't really know what to expect. I was really happy to come out on top."
Photo: PHOTOSPORT Venus Williams celebrates a win at Wimbledon.