Two judges gave it 115-113 for Alvares, while the other had it a 114-114 draw.
The fight, in front of a sellout, celebrity-studded crowd that included Mike Tyson, actor Will Smith and basketballer LeBron James at T-Mobile Arena, lived up to its billing as the best two pound-for-pound fighters in the world.
Golovkin landed some big blows to the head in the closing rounds, opening a cut above Alvares' left eye, but the Mexican prevailed to improve his career record to 50-1-2, including 34 knockouts.
Golovkin fell to 38-1-1, with 34 knockouts.
It was his first defeat since the 2005 world amateur championships.
"It was a very tight fight," said Alvares in a ringside interview after becoming the WBC, WBA, IBO and Ring Magazine world champion.
"I looked for a knockout but it's difficult. He's a great fighter but in the end I got the victory.
"I'm very excited, very emotional. I want to thank everyone who believes in me. This is for them and long live Mexico."
Kazakh Golovkin, 36, thought he had perhaps done enough to get the decision.
"I’m not going to say who won tonight, because the victory belongs to Canelo according to the judges," he was quoted as saying by ESPN.
"I thought it was a very good fight for the fans, and very exciting. I thought I fought better than he did."
ESPN boxing analyst Teddy Atlas agreed.
"There's no doubt about it. Golovkin won the fight," Atlas said. "At the end of the day it was the wrong decision..."
Golovkin was tentative early as Alvares dictated the terms, but the Kazakh got more aggressive as the bout progressed.
But Alvares landed more body punches, 46-6 by the official count, and more power punches, even as Golovkin landed more overall punches.
Both fighters were suitably bloodied by the end of a bruising encounter, after Alvares had somehow absorbed a series of blows to the head and chin, while Golovkin's puffy face offered proof that it had been a two-way street.
The fight came after an acrimonious weigh-in during which Alvares almost head-butted Golovkin, who is known affectionately through the boxing world as 'Triple-G'.
The bad blood between the pair has grown since Alvarez was temporarily suspended by the Nevada State Athletic Commission in April for testing positive for the banned substance clenbuterol, forcing a postponement of their planned May 5 rematch.
But they embraced at the end of Saturday's fight as the crowed waited in anticipation of the judges' verdict.
"One of the best fights I've ever seen," tweeted James.
(Reporting by Andrew Both in Cary, North Carolina; editing by Amlan Chakraborty)
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