World number one Swiatek continued her bid for a third Rome title in imperious style, dealing with American Keys in little more than an hour on a baking centre court.
"Today I'm really proud of myself because I feel like I'm playing better and for sure this was the best day for me in Rome," said Swiatek.
In the last four Swiatek will take on Zheng Qinwen or third seed Coco Gauff, who face off in the day's final match on centre court.
She maintained her red-hot form at the Foro Italico, where she has not yet dropped a set, ahead of her French Open title defence later this month.
The three-time Roland Garros champion arrived in Rome off the back of winning a third WTA 1000 title of the season in Madrid.
And she could yet become the first woman since Serena Williams in 2013 to win in the Spanish and Italian capitals in the same season.
'Unreal feeling'
Chile's Tabilo stunned 24-time Grand Slam champion Djokovic in straight sets on Sunday and made the quarter-finals after winning a hugely entertaining battle with Khachanov, 7-6 (7/5), 7-6 (12/10).
Tabilo reached the last eight of a Masters 1000 event for the first time and will next play qualifier Thiago Monteiro.
"Just being in my first quarter-final is an unreal feeling, just trying to soak it all in right now. It's a crazy feeling," said Tabilo.
The 26-year-old had a much harder time of it against 18th-ranked Khachanov, whose six tour titles have all come on hard courts, than against Djokovic.
Tabilo came through a thrilling second-set tie-break which featured 11 service breaks, two set points for Khachanov and five match points, exploding with joy after the winning volley.
"There was just so much nerves there, like feeling that arm really heavy and in the last few service points I was like 'I just gotta risk it all'," added Tabilo.
"With the win two days ago it's been crazy. I just had to turn off the phone and just kind of be with the team, be with the people close to me and I'm just happy that I was able to refresh the mind."
Next up for the men on centre court will be Alexander Zverev, who faces unseeded Nuno Borges in the men's last 16 for a quarter-final clash with Taylor Fritz.
Medvedev continues bid
American Fritz beat eighth seed Grigor Dimitrov after losing a 20-minute tie-break in the second set before eventually coming through 6-2, 6-7 (11/13), 6-1.
"It's easy to go back and I guess dwell on that the whole third set but I did a really good job in just putting it behind me," said Fritz.
Men's champion Daniil Medvedev faces Tommy Paul after coming through a gruelling match against qualifier Hamad Medjedovic on Monday.
The 28-year-old second seed has a great chance to retain his title as the men's tournament has been shorn of a host of big names, including the man he beat to last year's crown Holger Rune.
And with Madrid champion Andrey Rublev and the beaten finalist Felix Auger-Aliassime also falling, an event without the world's top three players is now wide open.
As well as Djokovic's early exit, Italian world number two Jannik Sinner and third-ranked Carlos Alcaraz withdrew injured before the tournament.
Also hoping to pounce is sixth seed and reigning Monte Carlo champion Stefanos Tsitsipas, who takes on Australia's Alex de Minaur.
