The veteran American, who gave birth to her first child during last year's US Open, got off to a shaky start and fell 3-1 down in the opening set before saving three break points in her next service game.
On the men's side, John Isner's bid to become the first American man in a dozen years to get to the final four at Flushing Meadows ended with a 6-7 (5), 6-3, 7-6 (4), 6-2 loss in Arthur Ashe Stadium to No. 3 seed Juan Martin del Potro, the Argentine who won the 2009 championship.
Serving for the match at 5-3 Williams didn't allow any room for doubt, holding at love with two aces and an overhead smash followed by one last ace.
Williams is only playing her eighth tournament since becoming a mum, but had only dropped one set - in her last-16 match against Latvia's Kaia Kanepi - on her way to the last eight.
"I still know that no matter whether I'm in the semi-finals or the finals, I have a really long way to go to win".
The evergreen Williams is just two matches from a grand slam title that would see her draw level with Margaret Court as the sport's all-time leader.
Sevastova retired in 2013, returned to the game in the same year and since then has played some of her best tennis in NY. But as Williams started to find her groove she held and then broke serve to tie it 4-4.
Once she'd overcome the early difficulties, Williams was a joy to behold.
Rafael Nadal was forced to go the distance in an epic five-setter against Dominic Thiem in their US Open quarter-final, while Serena Williams fought back to beat Karolina Pliskova and reach the semi-finals in NY.
Sep 4, 2018; New York, NY, USA; Serena Williams of the United States hits a forehand against Karolina Pliskova of the Czech Republic (not pictured) in a quarter-final match on day nine of the 2018 U.S. Open tennis tournament at USTA Billie Jean King National Tennis Center. He was knocked out before the quarterfinals of a major event for the first time since he lost in the third round of the 2015 Australian Open. "I mean, there is still semi-finals", she said. It's still long way to go, I think.
"When you don't play the big points well and don't take your opportunities early, that could affect the outcome of the match", Stephens said. He committed back-to-back double faults to fall behind 4-1, and he eventually lost on another error. "I don't think there's any change with her game", Pliskova said. But I got out of a tough second set and really found my feet and chose to be a little more aggressive.
The most noticeable improvement in Pliskova's game since her 2016 semifinal shock upset over Williams is her movement around the court.
She could be ranked as high as 11th by the end of play Saturday, should she make 2018 her seventh US Open crown.