In a first set dominated by the server, it was Nadal who grabbed a late break to eventually take the first set with Tsitsipas returning the favor in the second set before the Spaniard ran away with the third set.
Nadal reaches last four in London after win over Tsitsipas
The first six games yielded little progress for the returner as each man came out serving strong. It was Nadal who had the first break opportunities of the set after clubbing a forehand to set up 15-40. Tsitsipas took control, some strong passing shots getting him out of trouble.
He wasn't as fortunate the next time he served as a wicked slice from Nadal drew a backhand error from the Greek and a double fault on break point gave the Spaniard a 5-4 lead. Serving for the set, he pounded down consecutive unreturnable serves from 30-30 to take the lead.
Tsitsipas saved a break point in the opening game of the second set and after that, both men resumed holding comfortably, the Greek only needing to fend off challenges from 30-30 in two games. After winning one point through four games in the set on Nadal's serve, the sixth seed broke when the second seed double faulted on set point.
With the match now level, the beginning of the third set would be key and three successive breaks gave Nadal a 2-1 lead, the last of those coming after Tsitsipas sprayed a backhand wide. After an exchange of holds, the Spaniard finished strong, winning the final three games, setting up a last four encounter with Daniil Medvedev.