Pablo Cuevas also lost on a light day of action.
Both recorded straightforward Monday victories.
Underdogs Alexandra Dulgheru, Elena-Gabriela Ruse and Miriam Bulgaru all fell.
The American will play Kevin Anderson on Friday after his four-set win over Milos Raonic.
The Canadian visibly struggled with a leg problem in the final set of his quarterfinal loss to John Isner.
The American came through in four sets in a match replete with aces and quick points.
The Latvian smashed 32 winners in the 7-5, 6-4 victory.
She extended her Wimbledon winning streak, which dates to 2015, to 17 matches.
The world No. 1 won the last nine games.
The two players left the court Wednesday evening with Cilic in complete control.
The No. 2 seed asserted she was the victim of a tough draw and an opponent who had a spectacular day.
She led 5-1 in the third and had four match points on her serve before squandering all of those chances.
The former world No. 1 reached her maiden Wimbledon third round with an impressive performance.
Naomi Broady proved a game opponent on home lawns.
He stormed from behind on countless occasions to win the day's standout match.
Sam Querrey and Milos Raonic had no trouble in opening round victories.
The onetime top 5 player is seeking his first Wimbledon quarterfinal.
Surprise semifinalists Marco Cecchinato and Mikhail Kukushkin each fell a match short of Saturday's final.
They defeated Gael Monfils and Jiri Vesely, respectively, in Friday's semifinals.
The two Frenchmen will face off in Friday's semifinal round.