Ostapenko, the 2017 French Open champion who's previous best at the All England Club was the quarter-finals a year ago, remained on course to land her second Grand Slam title thanks to a relatively comfortable win on No 1 Court.
Ostapenko made it three on the bounce shortly afterwards though and sat down with an air of confidence to suggest she had the match under control.
It was Serena's 100th career main draw victory on grass. She said afterwards: "These 10 days just brought me so much joy".
"But this is only my fourth tournament back, I don't feel pressure, I don't feel I have to win this, I don't feel I have to lose this". Just going to prepare well for the match.
Twice Grand Slam victor Kerber, 30, will next face Latvian 12th seed Jelena Ostapenko in the last four on Thursday.
While her serve wasn't at the level that she would have wanted, Ostapenko getting the lead was key to improving her second serve.
Serena Williams has lost a set for the first time at this Wimbledon.
Williams will take on No.13 seed Julia Gorges of Germany, who also managed a comeback win against Kiki Bertens 3-6, 7-5, 6-1 to make her first appearance in the semifinals at the All England Club.
Over the last week, Kerber has watched all the top 10 seeds perish, which has raised expectations that she could repeat her 2016 run here to the final. "She didn't let me play how I wanted", said Cibulkova, the world number 33.
She won the grass-court tournament the last two times she played it, in 2015 and 2016, before missing it previous year while pregnant.
Williams has yet to face a player ranked inside the top 40 in the tournament, but that will change in the semifinals.
She and Ostapenko have never played each other before and it should be a classic encounter between the German counter-puncher and all-out attack of the Latvian. I'm just going out there and enjoying it.
Latvian Jelena Ostapenko, yet to lose a set in this year's tournament, blew away Dominica Cibulkova 7-5 6-4 to become the first player from her country to reach a singles semi-final at the All England Club.
She hasn't dropped a set yet, has spent less than five hours in total on court through her first four matches, is averaging a 24 winner-count in each round, yet somehow Jelena Ostapenko has been flying under the radar at Wimbledon this fortnight. Even when I was down in the first set, I thought, "Well, she's playing great, [but] I'm doing a lot of the right things".
The match was suspended on Monday evening due to fading light, with the Argentine star two sets to one ahead.
Del Potro looked flat as he was broken to trail 3-1 but he clawed his way back to lead 5-4 with his serve to come.
"I don't think Kasatkina has been disciplined enough".