The 26-year-old Russian can overtake Novak Djokovic for top spot in the men's tennis rankings if he wins the title here.
Medvedev, who won the 2021 US Open and was a runner-up to Rafael Nadal last month at the Australian Open, is playing in Mexico for the first time.
"It's not easy to come back after some rest and some time off competition,'' said Medvedev, who rallied from a break down in the second set for victory. "I managed to fight until the end against a very tough opponent, and I'm happy that I managed to win.''
If Medvedev wins this tournament -- or if he reaches the Acapulco final and Djokovic does not win the title at Dubai -- he will become the first player other than Djokovic, Roger Federer, Nadal or Andy Murray to hold the top spot since 2004.
Medvedev admitted he is thinking about the milestone but acknowledged that it might not happen next week.
"I know that in the next three tournaments it can be a possibility, and that's why I'm going to try to do this, because it's not a dream anymore, it's a goal," he said. "And I will try to play well in the next three tournaments to achieve it.''
The likely biggest challenge for Medvedev in Mexico could be fourth-seeded Nadal, who opened with a 6-3, 6-2 win over Denis Kudla.
Nadal, who has won three titles in Acapulco (2005, 2013 and 2020), next faces Stefan Kozlov on Wednesday.
Medvedev could meet Nadal for the first time since the Australian Open final in the Acapulco semifinals. Nadal rallied to win the final at Melbourne Park in five sets to capture a men's record 21st Grand Slam singles title, breaking a tie with Federer and Djokovic. It also prevented Medvedev from becoming the first man in the Open era to win his second major title at the very next Grand Slam event.
Nadal initially said after winning the Australian title that he was considering skipping Acapulco to rest his body in order to play at Indian Wells, but he later decided to travel to Mexico once again.
"In the last few years, I have played less tournaments ... and now I do it where I feel like, and at this stage in my career, this is a place [that] leaves me feeling good,'' Nadal said.
Unlike Medvedev, the 35-year-old Nadal said the top ranking is no longer something he craves.
"That time has passed for me. I think that all my physical problems took that chance away from me, and I'm no longer chasing that goal, it would be a mistake for me to chase it," Nadal said. "If I can do it while playing only on the tournaments that I can, I would be very happy.''
He said that's unlikely, given the number and quality of the younger players who can participate in more tournaments than he can.
In other matches on Tuesday, Stefanos Tsitsipas defeated Laslo Djere 7-6 (7) 7-6 (4), Tommy Paul advanced to a meeting with Dusan Lajovic when fifth-seeded Matteo Berrettini retired from their match in the second set because of an abdominal injury, and Yoshihito Nishioka beat Feliciano Lopez 2-6, 6-0, 6-4.
Berrettini, who reached the semifinals in the Australian Open, won the first set 6-4 but was down 5-1 in the second when he withdrew.
The Mexican Open, a 500 tournament, is played on the hard courts of the GNP Arena in Acapulco, a popular tourist destination south of Mexico City.