The pair were granted a wild card after Murray pulled out of the singles due to his failure to regain full fitness.
The Russian looked out of sorts early on Centre Court as he lost the first set.
Defending Wimbledon champion Carlos Alcaraz made a shaky start against unseeded Australian Aleksandar Vukic but moved through the gears to seal a 7-6(5) 6-2 6-2 victory and power into the third round on Wednesday.
Playing with a support on his right leg following a minor operation less than four weeks ago that cut short his French Open, the 37-year-old made a solid start and drew first blood in a marathon fourth game.
The Spanish third seed was taken to a tie-break in the opening set and trailed 2-0 against his unheralded opponent in the second but held his nerve to win 7-6 (7/3), 7-5, 6-2.
Medvedev, a semi-finalist last year, hit 16 aces in his 6-3, 6-4, 6-2 win over Aleksandar Kovacevic of the United States.
Alcaraz, 21, beat Novak Djokovic to the title a year ago and has since taken his Grand Slam haul to three after winning the French Open earlier this month and despite being seeded three will be favourite to rack up number four.
The Serbian is bidding for a record 25th Grand Slam title.
Novak Djokovic will play at Wimbledon after being named in the draw on Friday, despite concerns over his fitness following his withdrawal from the French Open.
The pair were granted a wild card after Murray pulled out of the singles due to his failure to regain full fitness.
The Russian looked out of sorts early on Centre Court as he lost the first set.
Defending Wimbledon champion Carlos Alcaraz made a shaky start against unseeded Australian Aleksandar Vukic but moved through the gears to seal a 7-6(5) 6-2 6-2 victory and power into the third round on Wednesday.
Playing with a support on his right leg following a minor operation less than four weeks ago that cut short his French Open, the 37-year-old made a solid start and drew first blood in a marathon fourth game.
The Spanish third seed was taken to a tie-break in the opening set and trailed 2-0 against his unheralded opponent in the second but held his nerve to win 7-6 (7/3), 7-5, 6-2.
Medvedev, a semi-finalist last year, hit 16 aces in his 6-3, 6-4, 6-2 win over Aleksandar Kovacevic of the United States.
Alcaraz, 21, beat Novak Djokovic to the title a year ago and has since taken his Grand Slam haul to three after winning the French Open earlier this month and despite being seeded three will be favourite to rack up number four.
The Serbian is bidding for a record 25th Grand Slam title.
Novak Djokovic will play at Wimbledon after being named in the draw on Friday, despite concerns over his fitness following his withdrawal from the French Open.
The 21-year-old overcame a forearm issue to bag his first French Open title, emulating greats including Rafa Nadal, Roger Federer, Novak Djokovic and Andre Agassi with major wins on clay, hard and grass courts.