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The 20-year-old Alcaraz will need to beat Medvedev in his final group game on Friday.
The earlier Green Group clash was a non-event as Stefanos Tsitsipas retired injured against Holger Rune.
Rublev, ranked fifth in the world, began to despair after losing the first set and failed to put up much of a fight in the second.
Jannik Sinner made a dream start in front of his home crowd with a 6-4, 6-4 defeat of Stefanos Tsitsipas in their opening Green Group clash.
Fittingly the London era ended as it began with a Russian winner after Nikolay Davydenko took the 2009 title.
Rafael Nadal's dream of a first ATP Finals title and Novak Djokovic's quest for a record-equalling sixth vanished in defeats by Daniil Medvedev and Dominic Thiem in two seismic semifinals.
The 27-year-old Austrian appeared to be sliding to defeat when he trailed 0-4 in the third-set tie-break but stormed back to claim a 7-5, 6-7(10), 7-6(5) victory in just under three hours.
World No. 1 Novak Djokovic beat Alexander Zverev 6-3, 7-6(4) to seal a last-four spot.
The Spaniard beat defending champion Stefanos Tsitsipas 6-4, 4-6, 6-2 in the last round-robin match in the London Group.
The Russian was ice cool as he closed out victory to make it two wins from two in the group and guarantee a semifinal berth.