The 24-year-old’s 6-3, 6-4 win put him joint top of the Tokyo Group alongside world number one Novak Djokovic, who put on a masterclass to trounce debutant Diego Schwartzman 6-3, 6-2.
Medvedev will face Djokovic on Wednesday and will take heart from the fact that the Serb also lost all three of his group matches on his debut in 2007 but returned a year later to beat Nikolay Davydenko to claim the title in Shanghai.
Djokovic has won four more titles since the event moved to London in 2009 and, judging by the way he clicked smoothly into gear on Monday, will take some stopping as he bids to equal the six of Roger Federer.
Medvedev will not be short of confidence though after a superb display against Zverev who once again struggled to control his serving gremlins.
Is this the first underarm serve that @TheO2 has seen? 🤔🇷🇺 @DaniilMedwed delivers the Moment of the Day!… https://t.co/3MbHPAzdqN
— ATP Tour (@atptour) 1605565873000
“I actually didn’t know that he (Djokovic) was 0-3 in his first appearance,” Medvedev, who also beat Zverev to win this month’s Paris Masters, told reporters.
“I also saw today that he’s won 12 consecutive opening (group) matches at the ATP finals so hopefully I can do the same.
“I like to play against Novak and I’m looking forward to it.”
The opening games against Zverev were curious.
Medvedev gifted up his first service game with a double-fault, then Zverev served three double-faults in succession to hand the break back. Medvedev, initially struggling with his forehand, then survived a break point in the third game, winning a brutal rally with some incredible court coverage.
Sum up @DaniilMedwed’s performance in one word ⬇️📹: @TennisTV | #NittoATPFinals | #ATPTourhttps://t.co/A5TH7xYoW9
— ATP Tour (@atptour) 1605563151000
Zverev worked overtime trying to stay level at 2-3, only to throw away the game with consecutive double-faults.
From then on Medvedev was too solid, taking the first set with an ace and breaking in the seventh game of the second set as Zverev again wavered.
Medvedev, one of the sharpest thinkers on a tennis court, threw in an underarm serve at 4-3, 30-30 but served out in more conventional fashion at 5-4 to seal the win.
“Since the restart it was one of my worst matches,” Zverev, who will need to beat Schwartzman on Wednesday to stay in the hunt, told reporters.
“It was not good enough to beat a top 10 player today. If I play like today I won’t win any matches this week.”
Just as fellow debutant Andrey Rublev was easily dispatched by Rafa Nadal on Sunday, Schwartzman was powerless to stop Djokovic on a court that could have been made for his game.
Djokovic dropped his serve early on at the virtually empty O2 Arena, where on Sunday he was presented with the ATP’s end-of-year number one award for a record-equalling sixth time.
But from that moment on he was immaculate.
Classy as always from @dieschwartzman 👏#NittoATPFinals | #ATPTour
— ATP Tour (@atptour) 1605546828000
He broke back immediately and then pounced again when Schwartzman served at 3-4, outmanoeuvring his opponent before pummelling away a forehand winner into the corner.
With no fans in the 18,000 arena to rally to the Argentine’s underdog cause, world number nine Schwartzman never looked capable of extending the contest.
Djokovic secured two breaks in the second set and clinched victory with a minimum of fuss.