Medvedev finished with 10 aces as he reached his eighth quarter-final at the Masters level – all achieved since 2019.
Shapovalov has now dropped three matches in a row, at Wimbledon and last month in the Swiss alpine village of Gstaad where he was top seed.
Harris, who beat world number four Dominic Thiem and Denis Shapovalov en route to the final in Dubai in March, pulled off another upset by ousting Dimitrov 6-3, 3-6, 7-6 (7/5).
World number three Medvedev was the top seed for this week's tournament following his run to the Australian Open final but was dumped out 7-6 (7/4), 6-4 in just over 90 minutes by Serbian Lajovic, currently ranked 27th.
The world number three was the top seed for this week's tournament after arriving in the Netherlands following his run to the Australian Open final but was dumped out in just over 90 minutes by Serbian Lajovic, currently ranked 27th.
French Open 2020: Paris bubble not a real bubble, but French capital remains off-limits for players, coaches
Players, coaches and others are not getting the chance to sightsee or stroll, eat at their favourite brasserie or enjoy a croissant at a sidewalk cafe during the 15-day #RolandGarros
Italian Open 2020: Novak Djokovic, Rafael Nadal enter quarter-final; Simona Halep, Karolina Pliskova also through to last eight
Nadal proved too strong for 25th-ranked Lajovic, who had valiantly but vainly launched a fightback after trailing 4-0 in the second set to the Spaniard.
Italian Open 2020: After US Open run, Shapovalov piling up wins in Rome, Azarenka double bagels Kenin
After spending more than 22 hours on court over the previous two weeks at the US Open, where he reached the quarterfinals in both singles and doubles, Shapovalov is still going strong after crossing the Atlantic.
Australian Open 2020: Novak Djokovic breezes past Yoshihito Nishioka in straight sets, will face Diego Schwartzman in fourth round
In the fourth round, Djokovic will meet Argentine Diego Schwartzman, who beat Serb Dusan Lajovic 6-2, 6-3, 7-6(7) earlier on Friday
Australian Open 2020: Fears of bushfire smoke disrupting season's first Grand Slam recede as air quality improves in Melbourne
The Air Quality Policy for the Australian Open was made public on Friday with its thresholds for suspending play, although the referee still maintains the ultimate discretion to keep the players on the court
ATP Cup 2020: Novak Djokovic beats Rafael Nadal, later teams up with Victor Troicki to secure Serbia’s victory in final
Novak Djokovic beat Rafael Nadal and then went back on court within an hour and won the deciding doubles encounter to secure Serbia's victory over Spain in the inaugural ATP Cup final.
ATP Cup 2020: Novak Djokovic edges Daniil Medvedev in high quality three setter, Serbia progress to final
Novak Djokovic beat Daniil Medvedev 6-1, 5-7, 6-4 to secure Serbia's win over Russia and a spot in the final of the new ATP Cup.
Djokovic, who has won a record seven Australian Open men's singles titles, was playing in Sydney for the first time in a decade after going 3-0 in singles in the ATP Cup group stage in Brisbane.
ATP Cup 2020: Spain clinch fifth spot for the quarterfinals after Roberto Bautista Agut victory denies Japan
Spain advanced to the quarterfinals of the ATP Cup even before Rafael Nadal stepped on to the court Wednesday at the Perth Arena.
Shanghai Masters 2019: Andrey Rublev upsets 12th seed Borna Coric in straight sets; Matteo Berrettini through to second-round
It was a 36th win of the season for the 11th-seeded Berrettini who has now won 30 of those matches since defeating Struff on 22 April
French Open 2019: Alexander Zverev's nervous five-set win over Dusan Lajovic underlines his constant tussle with self
Nerves have been Zverev’s undoing before. For all his experience, his immense skill and his intense match-winning ability, Zverev is still young, and no matter how good, or how experienced you are at your job, losing focus is something that can happen to anyone.
French Open 2019 men's singles round-up: Alexander Zverev struggles past Dusan Lajovic in five-setter; Novak Djokovic strolls into round four
It took Alexander Zverev all five sets again as he advanced into the fourth round of the French Open with a 6-4, 6-2, 4-6, 1-6, 6-2 victory over Serbian Dusan Lajovic
Monte Carlo Masters: Fabio Fognini breaks free from lackadaisical demeanour to emerge as massive threat to clay-courters
Fognini threw in his share of out-of-nowhere drop shots and tougher-than-they-needed-to-be volley winners, but his consistency was the single most important differentiating factor in securing the title
Monte Carlo Masters: Fabio Fognini beats Dusan Lajovic in final to become first Italian in 51 years to win title
Italy's Fabio Fognini thrilled a crowd composed mainly of his countrymen as he defeated Dusan Lajovic 6-3, 6-4 to win the Monte Carlo Masters.
Monte Carlo Masters: Rafael Nadal endures 'worst clay court match' as Fabio Fognini storms into final
Rafael Nadal crashed out to Fabio Fognini in the Monte Carlo Masters semi-finals with the Spanish star admitting his loss was his 'worst clay court match'.