World No. 3 Alcaraz beat Rublev 6-3, 7-6 (10/8) to lift himself off the bottom of the John Newcombe Group.
Alexander Zverev opened his campaign at the ATP Finals in Turin on Monday evening by dispatching Andrey Rublev 6-4, 6-4 in their round-robin opener.
Three-time Grand Slam champion Stan Wawrinka rolled back the years on Friday as the 39-year-old ousted top seed Andrey Rublev to reach the Stockholm semi-finals.
Alcaraz and Tsitsipas will face each other in the French Open quarter-finals.
Russian sixth seed Andrey Rublev admitted he "lost it completely" as he suffered meltdown in a surprise third round exit from the French Open at the hands of Italian Matteo Arnaldi on Friday.
Czech teenager Jakub Mensik stunned top seed Andrey Rublev in straight sets at the Qatar Open on Thursday to reach his maiden ATP semi-final
Fourth-seed Jannik Sinner beats fifth-seed Andrey Rublev to reach Australian Open semi-finals.
Fifth seed Andrey Rublev tamed a battling Alex de Minaur in five gruelling sets to shatter home hopes and make his second successive Australian Open quarter-final on Sunday
World number five Andrey Rublev survived a huge scare on Friday to reach the semi-finals of the Hong Kong Open.
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