Taylor Fritz missed out on claiming the last spot at the ATP Finals in Turin later this month after squandering two match points in his Paris Masters quarter-final defeat to Carlos Alcaraz.

Fritz would have reached the end-of-season event in Italy at Rafael Jodar's expense had he beaten Alcaraz to make the last four.

He looked poised to do that after twice finding himself a point from victory in the second set, once on his opponent's serve at 5-3 up and then on his own with the score at 5-4.

However, Alcaraz rallied during a high-quality match to triumph 6-7 (10-12) 7-5 6-3 and ensure he will be joined by compatriot Jodar at the ATP Finals from November 15-22, live on Sky Sports.

Tommy Paul's three-set defeat to fellow American Ben Shelton earlier in the day - US Open finalist Shelton prevailing 6-4 4-6 6-3 - had ended his hopes of reaching the ATP Finals, with countryman Frances Tiafoe's place subsequently secured.

Fritz was looking to become the third US representative in this year's Turin showpiece, after Shelton and Tiafoe, but squandered a golden opportunity to get there and also defeat Alcaraz for just the second time in eight attempts.

The 29-year-old won the first set after a lengthy tie-break and then broke Alcaraz to open up a 4-3 lead in the second set, before saving a break point to make that 5-3.

Alcaraz had already qualified for the ATP Finals - an event he is yet to win in three previous tries - alongside world No 1 Alexander Zverev, Daniil Medvedev, Flavio Cobolli, Arthur Fils, Shelton and Tiafoe.

Home hopes in Turin will rest on Cobolli, with Jannik Sinner - who on Friday announced a split with coach Darren Cahill after five years - ending his campaign early due to a knee problem that has sidelined him since winning Wimbledon in July.

Alcaraz will face Casper Ruud in the semi-finals in Paris after the Norwegian saw off Portugal's Nuno Borges 7-6 (7-5) 6-4, with Shelton meeting home player Luca Van Assche, who overcame Australian qualifier - and Novak Djokovic's conqueror - Rinky Hijikata 6-4 6-7 (4-7) 7-5.

Should we get an Alcaraz-Shelton final in France, it would be a repeat of their five-set epic in the US Open quarter-finals, a match Shelton won in a final-set tie-break at Flushing Meadows.

Alcaraz said after fighting back against Fritz: "I tried not to let myself down in those difficult moments - to stay strong mentally.

"We played incredible tennis, both of us, and I used the energy of the people to give them what they wanted to watch. To entertain them."