Chile's Tabilo stunned the tennis world by dismantling 24-time Grand Slam champion Djokovic in straight sets on Sunday and he made the Foro Italico last eight after a hugely entertaining match in which Khachanov played a full part.
Tabilo has reached the quarter-finals of a Masters 1000 event for the first time in his career and will fight for a spot in the last four against either China's Zhang Zhizhen or qualifier Thiago Monteiro.
He had a much harder time of it against 18th-ranked Khachanov, whose six tour titles have all come on hard courts, than he did against Djokovic.
Tabilo came through after a thrilling tie break in the second set which featured 11 service breaks, two set points for Khachanov and five match points, exploding with joy after the volley which won him the match.
Tabilo will be followed on centre court first by women's world number one Iga Swiatek and then Alexander Zverev who faces unseeded Nuno Borges in the men's last 16 for a quarter-final clash with Taylor Fritz who beat eighth seed Grigor Dimitrov 6-2, 6-7 (11/13), 6-1.
Top seed Swiatek continues her bid for a third Rome title with a quarter-final clash against American Madison Keys, ahead of her French Open title defence later this month.
The three-time Roland Garros champion, who arrived in the Italian capital off the back of winning a third WTA 1000 title of the season in Madrid, is yet to drop a set.
The winner of that match will play either Zheng Qinwen or third seed Coco Gauff who face off in the day's final match on centre court.
Medvedev faces Tommy Paul after coming through a gruelling match against qualifier Hamad Medjedovic on Monday.
The 28-year-old 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 being dumped out early, Italian world number two Jannik Sinner and third-ranked Carlos Alcaraz withdrew with injury 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.
