Fourth seed Medvedev had won all his previous matches against Rublev in straight sets and it was no different at a scorching Rod Laver Arena on Wednesday.
Nadal had a solid start, but the 35-year-old struggled physically towards the end of the contest
Nadal surpassed the haul of Roger Federer and Novak Djokovic.
Nadal faced no break points in a ruthless display to set up a meeting with Canadian Denis Shapovalov.
Next up for the 35-year-old will be another American in 39th-ranked Tommy Paul with a potential semi-final clash against top-seeded Russian Daniil Medvedev, who he defeated in the Australian Open final from a two-sets deficit.
Nadal, playing his first match since losing to Roger Federer in the Wimbledon semi-finals, fell behind 5-2 in the tiebreak before roaring back to prevail in his first career meeting with world number 53 Evans.
Images from Day 9 of the 2022 Australian Open, at Melbourne Park, on Tuesday.
World number one Rafael Nadal has been drawn alongside defending champion Alexander Zverev, Association of Tennis Professionals (ATP) reported.
Zverev was left wondering why he has been struggling to get into his matches
Novak Djokovic will begin his Australian Open title defence against Frenchman Jeremy Chardy, while reigning women's champion Sofia Kenin meets wild card Maddison Inglis, following the draw for the year's first Grand Slam on Friday.
This year's Australian Open will be allowed to admit up to 30,000 fans a day, around 50% of usual capacity, amid the COVID-19 pandemic.
Unvaccinated tennis star Novak Djokovic won the right to take his fight against deportation from Australia to a Federal Court on Saturday after the government cancelled his visa for the second time over COVID-19 entry regulations.
Italian top seed Matteo Berrettini marked himself down as a genuine Wimbledon threat after beating Britain's Cameron Norrie 6-4, 6-7(5), 6-3 to win the Queen's Club title on Sunday.
She is the second Swiss player to win the tournament after Martina Hingis won the inaugural edition in 2001.
With professional tennis tours closed down until mid July at the earliest because of the coronavirus pandemic, an esports version of the claycourt event is being staged online. Nadal showed impressive fingerwork to beat young Canadian Denis Shapovalov in his opening round-robin match on a digital representation of the Spanish capital's Manolo Santana Stadium.
A summary of Sunday's matches at the French Open.
A summary of Wednesday's action at the US Open on Day 3.
World number one Novak Djokovic was disqualified from his US Open fourth round match against Pablo Carreno Busta on Sunday after the Serbian struck a line judge with a ball following a point.
IMAGES from Day 2 of the US Open played at Flushing Meadows in New York on Tuesday.
Images from Day 8 of Wimbledon 2022 at the All England Lawn Tennis and Croquet Club in London, on Monday.
List of French Open men's singles champions:
World number one Novak Djokovic extended his winning run in Asia when he strolled into the last-16 of the Shanghai Masters.
Alexander Zverev snatched the Laver Cup for Team Europe as he beat Canada's Milos Raonic in the final rubber of a thrilling three days of action in Geneva's Palexpo Arena on Sunday.
Thiem, Wawrinka stay positive after defeats on return
Nadal has a habit of truly coming into his own at Roland Garros, as his 100-2 win-loss record testifies.
After a brief interruption when the players were locked at 5-5 in the opening set, Federer saved two set points in the tiebreak and held firm to gain the upper hand in the contest.
Images from the action on Day 2 at the Australian Open.
A summary of the action on Day 3 at the US Open.
The French Open witnessed a stunning upset on its very first day as 18-year-old Anastasia Potapova outclassed Angelique Kerber 6-4, 6-2 in the first round match on Sunday.
Facing the prospect of empty stands at the first fanless Grand Slam since the coronavirus outbreak, top contenders at this year's US Open admit that the unprecedented new hush will take some getting used to.
Ash Barty's bid to end the host nation's long wait for a homegrown Australian Open champion will begin against Ukraine's Lesia Tsurenko
Images from Day 3 of the 2020 US Open in New York, on Wednesday.
Roger Federer and Serena Williams, holders of a combined 43 singles Grand Slam titles, will face each other for the first time on Tuesday when they feature in the Hopman Cup mixed doubles match.
Djokovic has never failed to win the tournament after making the semi-finals and he will be heavily favoured to claim a record-extending ninth title at his favourite Slam on Sunday.
Muguruza wins all-Spanish clash with Badosa at WTA Finals
The winners of the Serbia-Germany tie will join Spain, Russia and Italy in the semi-finals.
IMAGES from Day 6 of the Wimbledon Championships at All England Lawn Tennis and Croquet Club on Saturday.
The Murray bothers last played together at the 2016 Rio Olympics, and were a prolific partnership when Britain won the Davis Cup in 2015.
Serena Williams is unlikely to win a record equalling 24th Grand slam title on the claycourts of Roland Garros, although her chance will come, the American's long-time coach Patrick Mouratoglou said on Friday.
Gauff vows to be more aggressive in Osaka showdown
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