The contest at the Mandalay Bay Resort and Casino, carried live by streaming service Netflix, was a chance for both Spanish stars to test their fitness.
Nadal, a 22-time Grand Slam champion, missed most of last year with a hip injury sustained at the Australian Open.
He made his comeback at the Brisbane International in January before a small muscle tear forced the veteran to pull out of this season's first Grand Slam in Melbourne.
He shelved plans to return to action at the Qatar Open in February, saying he was "not ready to compete."
He told interviewer Mary Joe Fernandez he felt "much better than expected" after pocketing the first set against Alcaraz.
And he had enough in the tank to save five match points in the match tiebreak before Alcaraz finally finished it out.
It was an encouraging performance before Indian Wells, where Nadal is a three-time champion. In his most recent Indian Wells appearance, Nadal finished runner-up to American Taylor Fritz in 2022.
The Spanish veteran will play his first-round match at Indian Wells on Thursday. Alcaraz, who will be seeded in the California desert, will have a first-round bye.
Alcaraz, ranked second in the world, will be trying to become the first man to successfully defend his Indian Wells title since Novak Djokovic's three-peat from 2014-2016.
But the Spaniard has had his own injury concerns of late, retiring from his first-round match at the Rio Open less than two weeks ago after he rolled his right ankle on just the second point of the match against Thiago Monteiro.
It was another setback for the two-time Grand Slam winner, who fell to Alexander Zverev in the Australian Open quarter-finals and lost to Chilean Nicolas Jarry in the semi-finals at Buenos Aires.
Alcaraz hasn't won an ATP title since his stunning Wimbledon triumph over Djokovic last July.
