Nadal leads the head-to-head with Federer 23-14 but has not beaten the Swiss in 2017, losing in the finals of the Australian Open and Miami Masters and in the last-16 at Indian Wells.
The Spaniard was pushed hard by fourth seed Cilic, who put his booming forehand to good use but could not stop Nadal claiming a 16 consecutive victory.
"We are at the highest level of our sport, so nobody wins easy," Nadal said. "If you want to compete in the most important events... you're going to have tough matches and today was one of them."
Federer, the only man who can still stop Nadal ending the year as world number one, lost to Del Potro in the U.S. Open quarter-finals and looked set for a second consecutive defeat after tamely surrendering the first set.
The Swiss changed his approach in the second, following his serves into the net more often to take time away from the Argentine and the strategy worked as Del Potro failed to earn a single break point in the final two sets.
Nadal forced Cilic to save six break points in his first two service games, but the Croat hung on and passed up a glorious chance to go ahead himself when he squandered three break points with the score tied at 5-5 in the first.
Nadal then broke the world number five before serving out the set.
The Spaniard looked set for victory when he broke again early in the second, but Cilic drew level in the sixth game as Nadal pounded the net cord in frustration after missing an easy volley with his opponent stranded.
A flurry of Cilic errors gave Nadal three break points with the second set tied at 4-4.
The Croatian got out of trouble with three big serves but double faulted to hand the initiative back to Nadal and skied a forehand to give his opponent the chance to serve out the match.
Nadal failed to capitalise, squandering a match point before Cilic unleashed two massive forehands to level again at 5-5 as the set headed towards a tiebreak where Nadal's ability to hold his nerve in clutch situations proved the difference.
(Writing by Simon Jennings in Bengaluru; Editing by Ken Ferris)
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