In the first set, the 26-year-old Italian, playing in her first Grand Slam quarterfinals, had Williams scrambling after her lightning-quick serves and almost knocked her off of her feet with one that notched 118 miles per hour.
Goerges also battled back from a set down to beat Dutchwoman Kiki Bertens 3-6 7-5 6-1 in the last of the women's quarterfinals.
"I knew I had to be aggressive otherwise she would have opportunity for winners so I just went for my shots", Ostapenko said.
She'll face Germany's Julia Gorges in the semifinals on Thursday at the All England Club.
Ostapenko, the 12th seed, overpowered Slovak Dominika Cibulkova 7-5 6-4 to reach Wimbledon's final four for the first time, and without dropping a set.
Williams, now the world number 181 having slipped down the rankings following her maternity leave, is the lowest-ranked player to reach the Wimbledon quarter-finals in the open era.
But the 29-year-old has erased those painful memories with a superb run, capped by a come from behind success against Bertens in her first Grand Slam quarter-final.
Rare is the player who can produce Williams' sort of pace on serves - Giorgi's average speeds were actually faster on first and second serves, and she delivered the match's first three aces - and mirror her power in groundstroke exchanges at the baseline. "I play a great level today", she said.
Williams' latest match required only 62 minutes and was not much of a contest, a 6-2, 6-2 win in which she compiled a 30-5 edge in winners against Evgeniya Rodina, a qualifier from Russian Federation ranked 120th who was dealing with a bothersome left thigh.
A double fault and a superb Goerges forehand created break point in Bertens' next service game but she was again up to the task, producing two big serves.
Williams is chasing an eighth Wimbledon crown and the American star on Monday showed why she is the title favorite with a 6-2, 6-2 demolition of Evgeniya Rodina in the fourth round.
She will face German world number 10 Kerber on Saturday in a repeat of the 2016 showpiece won by Williams.
This is all brand new for Goerges, who had never even been to a Grand Slam quarterfinal before this week.
By the time a Goerges drop-shot drifted into net to present Serena with the decisive break in the sixth game of the second set, the contest had already been sapped of any drama and moments later the title favourite was waving to the crowd in celebration. Now I'm just relaxed, I take care of the family and my husband helps a lot, so that makes it much easier for me. Camila served brilliantly to reduce the tally but the Serena's unrelenting attack sustained the gap to 5-3. She manages to hold on to her serve, but she can ill-afford such mistakes if wants to get back into the match.
Serena Williams has surprised herself by reaching the semi-finals on her Wimbledon comeback. However, the 13th seed has proved she knows how to win a close match. For the first time at this year's Wimbledon, she had lost a set.
"Every match starts from zero", Goerges said of her semifinal matchup against Williams. "It's now all gone", Ostapenko said.
Williams has won her first five matches against unseeded opponents.