The last round-robin match in the London Group was a straight knockout with both men having lost to Dominic Thiem and beaten Andrey Rublev earlier in the week.
But it was Spaniard Nadal who always appeared the likely winner despite a lapse which allowed Tsitsipas to extend the contest into a decider at a near-deserted O2 Arena.
After a flurry of service breaks at the start of the third set, the 34-year-old Nadal pulled away to reach the semi-finals for the first time in five years.
As group runner-up behind Thiem, he will face Daniil Medvedev for a place in the final with the Russian assured of top spot in the Tokyo Group.
“In general this was a very positive match for me,” said Nadal, who despite winning 20 Grand Slam titles has only two runners-up places to show for his previous nine appearances at the ATP Finals. “Excited to be in the semi-finals.”