The world number one, who was beaten by Pouille the last time they met at the 2016 US Open, lost a close first set before saving two match points in a second-set tiebreak to level things up.
Nadal needed all his experience to keep Pouille at bay in the decider and the match looked to be heading for another tiebreak before he pounced to break Pouille’s serve for the first time to go 6-5 up in the third.
The Spaniard held his nerve to close out the match in clinical fashion after two hours and 31 minutes.
Earlier on Tuesday, Juan Martin del Potro stormed into round two with a comprehensive 7-6(4) 6-4 win over Uruguay’s Pablo Cuevas and will face third seed Grigor Dimitrov, who battled past Bosnian Damir Dzumhur 6-1 3-6 6-3.
Eighth seed Nick Kyrgios breezed past Nikoloz Basilashvili 6-1 6-2, the Australian serving 12 aces as he closed out the contest in under an hour.
John Isner, the number six seed, also pulled off a routine 6-2 6-3 victory over Tunisian qualifier Malek Jaziri, although two of the American’s unseeded compatriots bowed out.
Jared Donaldson fought hard against seventh seed Tomas Berdych, but ran out of steam in the decider as he went down 6-3 0-6 6-2.
Jack Sock was the other American eliminated and the 25-year-old will be disappointed he could not hold off Andrey Rublev despite comfortably winning the first set against the Russian.
Rublev bounced back to win 3-6 6-1 6-2 and will face Berdych next.