Alvarez lunged briefly at Golovkin at the weigh-in on Friday, saying his anger got the better of him.
Alvarez, the new WBA and WBC middleweight champ, led for the majority of the fight.
Canelo Alvarez won the middleweight title by the narrowest of margins Saturday night, taking a majority decision over Gennady Golovkin to hand the longtime champion his first loss as a pro. Alvarez blamed the failed tests on contaminated meat from his native Mexico.
"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.
Golovkin had been denied a win in the pair's first bout, feeling he deserved a win but having to live with a draw.
Golovkin landed a huge right in the 11th and pushed Alvarez to the ropes.
Both fighters made the division limit of this world middleweight clash - 159.6lbs, with Alvarez tipping the scales at 159.4lbs with Golovkin two pounds heavier.
"I showed my victory with facts", Álvarez said afterward through an interpreter. At first I aimed for the knockout, I didn't. "I'm satisfied with the way we did it today".
Both fighters were cut in the course of the bout, Canelo sporting a long laceration underneath his left eyebrow, with Golovkin cut around the right eye and with swelling to his high cheekbones. Very exciting. Canelo surprised us all with the come forward pressure game plan. "I think we controlled the fight. Every great fighter has a great rival".
Golovkin's trainer Abel Sanchez, meanwhile, admitted he hoped to see a third meeting between the two.
"It was very hard and [Golovkin] is a great fighter". "There was only one or two rounds between them". It's obvious that these two guys can make great fights.
Nearly immediately there was talk of a third fight between two middleweights who now know each other well.