Italian Lorenzo Musetti squandered five championship points in the second set but came back to stun top seed Carlos Alcaraz and win his first ATP Tour title in Hamburg.
Sweden's Elias Ymer replaced Berrettini in the men's draw.
A win for Nadal in Sunday's final will break a three-way tie with Novak Djokovic and Roger Federer and give him sole owenership of the record for most Grand Slam singles titles.
The 25-year-old, who will make his second appearance at the ATP Finals, defeated Australia's Alexei Popyrin 7-6(3), 6-3 in the opening round of the Vienna Open.
Novak Djokovic beat Italian Matteo Berrettini 6-7(4), 6-4, 6-4, 6-3 to win his sixth title at Wimbledon.
The 25-year-old took two hours and 36 minutes to get past the 14th-seeded Hurkacz.
The only other Italians to qualify for the elite season-ender were Corrado Barazzutti in 1978 and Adriano Panatta in 1975 and neither managed to win a match.
The six-time champion was not at his fluent best on Tuesday but ultimately had too much for Berrettini, who won just three games against Novak Djokovic in his opener.
Nadal put pressure on the underdog Italian's serve from the start but Berrettini saved six break points to set up a first set tie breaker.