Medvedev, on the second longest winning streak of his career, broke Rublev twice in each set and won the last five games on the hard court.
Djokovic couldn't defend his Australian Open title last month because he was deported from the country for being unvaccinated.
Novak Djokovic swept aside seventh-seeded Karen Khachanov 6-2, 6-2 to reach the semifinals of the Dubai Championships.
Top-ranked Novak Djokovic defeated Philipp Kohlschreiber 6-3, 6-1 while Stefanos Tsitsipas got the better of Nikoloz Basilashvili 6-1, 6-0.
Djokovic defeated Jaziri 6-1, 6-2 in what turned out to be a one-sided contest on Monday. The World No. 1 landed 22 winners and did not face a break point to improve to 14-0 this year after exactly one hour.
Roger Federer defeated Stefanos Tsitsipas 6-4, 6-4 in the final of the Dubai Championships on Saturday.
Federer is looking to become the second man in the professional era to reach 100 tour-level tournament tiles, joining Jimmy Connors, who won 109.
The two-time major champion had trouble with her serve and was beaten 6-3, 6-3 by 67th-ranked Kristina Mladenovic at the Dubai Championships.
The third-seeded Bautista Agut denied the second-seeded Pouille his own second title this year and a chance to break into the top-10 rankings for the first time.
It should be noted that Federer has won the tournament seven times, which accounts for the most number of Dubai Championships title lifted by any player.
Muguruza defeated the fifth-seeded Frenchwoman in their second quarterfinal in two weeks, with the Spaniard also winning after being a set down in Doha.
New Delhi: Andy Murray who is currently World No 3 at ATP rankings was recently seen at a posh hotel in Dubai. The tennis star from Britain who had taken part in the Dubai Championships
Dubai, United Arab Emirates: Defending champion Roger Federer stormed back from 4-1 down in the first set to beat Fernando Verdasco 6-4, 6-3 on Wednesday and claim a spot in the quarterfinals of the Dubai
Dubai, United Arab Emirates: Andy Murray was knocked out of the Dubai Championships on Thursday, losing to 18-year-old Borna Coric 6-1, 6-3 in the quarterfinals.Murray, who reached the Australian Open final at the beginning of
Dubai, United Arab Emirates: Playing for the first time since winning the Australian Open, Novak Djokovic came through with a 6-4, 6-4 win over Vasek Pospisil on Tuesday in the first round of the Dubai
DUBAI, United Arab Emirates: Roger Federer won a record sixth Dubai Championships - and 78th career title - by beating Tomas Berdych 3-6, 6-4, 6-3 in the final on Saturday. Federer, who maintains a home
DUBAI, United Arab Emirates: Third-seeded Roger Federer ended top-seeded Novak Djokovic's chance of defending his Dubai Championships title with a 3-6, 6-3, 6-2 semifinal win Friday. Federer will be looking for his sixth Dubai title
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