The 18-year-old left-hander played near-perfect claycourt tennis for three sets, becoming the youngest winner of a Masters Series title since Michael Chang in Toronto 15 years ago.
His victory in three hours seven minutes means Nadal will move to second in the ATP Champions Race, with only Roger Federer standing above him.
Nadal had seemed poised to win the Master Series title in Miami earlier this month, only for Federer to come back from two sets down to claim victory.
This time he made no mistake, although he admitted there were a few anxious moments.
"I was happy to win the Davis Cup last year but this is unbelievable, it's my first big title," said Nadal, who will make his Roland Garros debut next month after being injured the last two years.
"I was a little bit scared when he came back because it was the same situation as Miami, but finally I won it.
"If I can play like this at Roland Garros I can get a good result there."
Argentine sixth seed Coria was appearing in his third successive Monte Carlo final and he started confidently, breaking Nadal's serve in the opening game.
Coria held his own serve to lead 2-0 but Nadal, wearing a bright orange sleeveless shirt, won 12 of the next 14 games with the same stunning mixture of power and precision that enabled him to thrash French Open champion Gaston Gaudio 6-3 6-0 in the quarter-finals.
Hitting his forehand with fizzing topspin Nadal dominated the rallies from the baseline, dragging one of the fastest players in the men's game all over the court.
Even Coria's trademark drop shot had a hint of desperation about it as he fought to keep Nadal at bay.
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He took advantage of a dip in Nadal's level to roll through the third set without dropping a game in 32 minutes.
However, Nadal did not panic and he regained the initiative to take a 4-1 lead in the fourth set.
By this stage both players were playing superb tennis, Nadal cutting the sidelines with whipped forehands and Coria showing gazelle-like speed to stay in the rallies.
Coria counter-punched back to 4-4 as Nadal, winner of two claycourt tournaments already this year, began to show signs of fatigue.
He was not to be denied though. Coria netted a backhand volley at 15-30 when serving to stay alive at 5-6, handing the Spaniard two match points.
Coria saved the first but his lethal drop shot failed him when he needed it most on the second, allowing Nadal the chance to swipe a forehand down the line before collapsing in a heap.
"I was beginning to feel a bit tired in the third set," said Nadal. "But I think the experience of losing to Federer from two sets up made me concentrate even more.
"It could have got really tough if it had gone to five."
Coria said before the match that Nadal is the best claycourt player in the world at the moment and he repeated that assertion after losing Sunday's final.
However, he felt the result could have been different if the match had gone the full distance.
"I think he would have got tired if I could have made the match last a bit longer," said Coria, who won their only previous meeting two years ago in Monte Carlo.
"If I can keep this going I will be OK at the French Open."