Serena Williams routed the 18th-seeded Spaniard 6-0, 6-0 in just 52 minutes on Tuesday, Suarez Navarro's 25th birthday, to reach a matchup Friday with Li, the 2011 French Open champion who ousted Russian 24th seed Ekaterina Makarova.
Reigning French Open champion Williams, a 16-time Grand Slam winner seeking her fifth US Open crown and ninth title of the year, has dropped only 13 games in five wins on her way to the semis for a fifth US Open appearance in a row.
Asked if this was her most dominant US Open performance, Williams said, "I guess so. I haven't thought about it yet. I'm still in the tournament and I'm not thinking about, like, 'I'm really dominant now.'
"I'm just thinking, 'OK, I just have a really tough match in the next round and I really want to do well."
Williams, who would be the oldest women's champion in US Open history at age 31, matched the worst rout in US Open women's quarter-final history, Martina Navratilova's 6-0, 6-0 blanking of Bulgarian Manuela Maleeva in 1989.
Suarez Navarro, who has never taken more than three games off Williams in three career meetings, was the first Spanish woman in a US Open quarter-final since Arantxa Sanchez-Vicario in 1998.
Williams hit 20 winners while Suarez Navarro managed only 18 points in the match, just three off winners on a windy night at Arthur Ashe Stadium.
The Spaniard reached deuce for the first time as she served in the second game of the second set, coming within a point of holding when a fan yelled, "Come on Serena, give her a game. It's her birthday."
Instead, Williams broke for a 2-0 lead, drawing a couple of boos in a romp that for a few apparently had started to seem like bullying of a helpless foe.
Williams said that compassion was not a consideration at any point, giving up a pity game not in her thoughts at all.
"You don't really think about it," Williams said. "You just think about winning the points and winning the games. That's all you think about. At least, I don't think about anything else. Maybe after the match. During, I just try to stay in the moment."
A few boos came when Williams held to 4-0 and Suarez Navarro drew huge cheers when she forced two break points on Williams in the fifth game.
There was a major groan when the Spaniard netted a forehand on a break point chance as Williams went on to hold, receive polite applause after doing so and a typical roar from a generally supportive crowd after she won the match.
Williams would not call the performance flawless.
"Of course not. I played good, though," she said. "I was just more focused than anything. I like to believe there's room for improvement."
Asked what errors she had made, Williams replied, "I'm not here to say what I did wrong. I think I definitely played well, but she also gave me some good points."