Stefanos Tsitsipas reached the semi-finals of the ATP Finals, while Rafael Nadal produced a stunning comeback to boost his hopes of joining him.
Tsitsipas, 21, making his debut at the event, dominated defending champion Alexander Zverev in a 6-3 6-2 win.
Earlier, Nadal fought back from 5-1 down in the deciding set and saved a match point to beat fourth seed Daniil Medvedev 6-7 (3-7) 6-3 7-6 (7-4).
The Spaniard must beat Tsitsipas on Friday to have a chance of advancing.
Nadal, who is also looking to keep hold of the world number one ranking, could have been eliminated on Wednesday had he lost and his fate is still not in his own hands as he also needs Medvedev to beat Zverev in their match on Friday.
Nadal, 33, admitted he got “super lucky” to beat the Russian.
“This match is one of those that one [time] out of 1,000 you win,” Nadal said.
The last meeting between Nadal and 23-year-old Medvedev was September’s US Open final, which the Spaniard won in five sets, and this match was almost as thrilling.
Both players looked beaten at times, Medvedev when he was distracted while he was losing the second set and Nadal when a double-break down in the decider.
Errors from Nadal and a resurgence by Medvedev at the start of the third set led to the Russian racing into a 4-0 lead.
He had two break points for 5-0, and match point two games later, but 19-time Grand Slam champion Nadal showed all of his trademark fighting spirit, roared on by the crowd at London’s O2 Arena.
As Nadal clawed his way back, Medvedev lost focus again, sarcastically giving a thumbs-up to his box as games slipped away.
After losing five successive games, the Russian settled himself to force a tie-break and was on serve at 4-5 in the breaker before he dragged a short forehand wide to give Nadal a mini-break and match point.
Another gruelling rally followed but a Medvedev shot that was originally called in was ruled out by Hawk-Eye to hand Nadal victory after two hours 49 minutes.
Medvedev can still qualify for the last four if he beats Zverev in two sets on Friday and Tsitsipas beats Nadal.
Tsitsipas is the youngest player at this year’s ATP Finals, competing just a year after he won the NextGen tournament – the season-ending event for players aged 21 or under – but he produced a clinical, mature display to see off Zverev.
The pair were evenly matched in the first set until the Australian Open semi-finalist pounced when Zverev’s level dropped at 4-3, breaking serve and then closing out the match with his third game in a row.
Tsitsipas’ level increased further in the second set, hitting a backhand winner to bring up break point in the first game and then clinching it at the net after another well constructed point.
He broke again for 5-1 lead soon after with more immaculate tennis and even admitted afterwards he was “surprised” by his performance.
“I did everything right and once again it was not just me out there but a whole bunch of excited people who came to support me,” he said, referencing the strong support he received at the O2 Arena.
Zverev, meanwhile, was unable to find the high level that helped him sweep aside Nadal 6-2 6-4 on Monday.
The German lost his way badly after being broken in the first set and displayed negative body language on court.
He will still progress at Nadal’s expense if he beats Medvedev on Friday.
