Russian friends Medvedev and Rublev were destined for another epic showdown after meeting in the Dubai Open final and US Open quarter-finals, with world number three Medvedev winning both matches.
However, Rublev, ranked fifth in the world, began to despair after losing the first set and failing to put up much of a fight in the second.
"I played great before the tournament and I managed to put it in the court now. I felt really good and was able to get the upper hand fast," said Medvedev of his winning start.
"I like to played aggressive on my serve, but Rublev plays in such a style that he doesn't let me (have) any other option because I don't have the power of Alcaraz or (Stefanos) Tsitsipas on my forehand," he added.
Earlier on Monday, Zverev came from a set down to beat a sluggish Alcaraz after two hours and 32 minutes in their opener.
"My serve helped me a lot. Saving the break point in the first game of the second set helped me," Zverev said. "You don't want to go down a set and a break against the world number two, so I'm happy,"
The seventh-ranked German is making his sixth appearance at the event, having won the title in Turin in 2021 and London in 2018.
Zverev, who missed last year's edition due to a right ankle injury suffered during his Roland Garros semi-final against Rafael Nadal, fell when he hit a forehand and hit his ankle.
"I didn't twist my ankle. I slipped a little bit. There was a pain for a while and I don't think any damage was done. I hope not, we'll see when it calms down. It's nothing comparable to Paris."
