Daniil Medvedev booked his place in the last four of the ATP Finals on Wednesday after beating Alexander Zverev 7-6 (9/7), 6-4, while Carlos Alcaraz cruised past troubled Andrey Rublev to get his campaign up and running. World number three Medvedev had to win in straight sets to claim a spot in the semi-finals in Turin with a match to spare and he saw off big-hitting German Zverev in a stodgy Red Group encounter. He faces Carlos Alcaraz, a 7-5, 6-2 winner earlier in the day, in his final match and has the world number two's last-four hopes in his hands.