Golovkin started cautiously but had the edge in the middle rounds as the fight heated up and started to live up to its hype, eventually turning into a brutal and memorable encounter.
Alvarez, urged by his corner that he needed something special in the final few rounds, finished with a flurry as the capacity crowd cheered him on at T-Mobile Arena.
All three judges gave the Mexican the last three rounds.
Golovkin landed more punches over the 12 rounds and was ahead 218 to 169 overall by an unofficial count.
Both boxers said they were keen to fight again.
"Yes, of course, if the people want it," said Alvarez, who thought he had won "seven or eight" rounds.
"Look at my belts. I'm still the champion," he said. "Of course I want a rematch."
While many experts gave Golovkin the edge, the scorecard of the judge that awarded it to Alvarez 118-110 immediately raised eyebrows.
Another judge scored it 115-113 to Golovkin, while the third had it a 114-114 draw. The result was roundly booed.
The two best middleweights and two of the top pound-for-pound fighters in the sport offered contrasting styles.
Golovkin mostly occupied the centre of the ring, while Alvarez was more comfortable near the ropes, content for the most part to counterpunch.
California-based Golovkin, widely known by his nickname 'Triple G', had an edge in jabs, but neither fighter could deliver a knockout.
"I want big drama show. It’s not my fault," said Golovkin.
The result leaves Golovkin with a 37-0-1 career record, while Alvarez is 49-1-2, his only loss coming against Floyd Mayweather in 2013.
The fight was two years in the making before the two camps agreed terms and though Golovkin came in as champion, he accepted a smaller guarantee, reportedly $3 million (£2.2 million) to Alvarez's $5 million.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Peter Rutherford and Sudipto Ganguly)
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