Kovalev was the more aggressive of the two boxers and was winning the majority of the rounds heading into the seventh.
Kovalev got up quickly, but it only got worse from there as Alvarez (24-0, 12 KO's) rocked him with an uppercut and a hard jab that almost sent Kovalev's mouthpiece flying.
He then finished him off with a right hook and left uppercut combination and at that point the referee stepped in with 15 seconds before the bell in front of a crowd of 5,600 at the Hard Rock Hotel in Atlantic City, New Jersey.
After the fight, Kovalev was transported to the hospital.
"I never said that I don't want to fight this guy because he's very strong". I feel OK. Thank you everyone, thank you very much to all the fans around the world for your support.
After a feeling-out round in the first, Kovalev applied pressure quickly to start the second, making Alvarez eat punches and cutting off the ring.
You can forget about that all-Russian showdown between Sergey Kovalev and Dmitry Bivol for the unified light heavyweight championship.
Welterweight Enriko Gogokhia (7-0, 3 KOs), 27, a southpaw from the Republic of Georgia fighting out of Los Angeles, got in six rounds of work in a shutout of Ronald Montes (18-10, 16 KOs), 32, of Colombia, in an action-free fight.
If Kovalev takes an extended break, that could afford Alvarez an opportunity to make an optional title defense in Quebec.
He dominated future Hall of Famer Bernard Hopkins via a lopsided unanimous decision in November of 2014 and has two knockout victories over former light heavyweight champion Jean Pascal. Alvarez, who once had surgery on his right hand, found the power in that hand to level Kovalev with a right and send him to the canvas. "It was a great accomplishment [for Alvarez], so I don't want to make those kinds of judgments".
It was another test for young Dmitry Bivol, the light heavyweight division's top young star at the moment, but he passed the test that was Isaac Chilemba with flying colors.
Kovalev regained one of his old titles last November following Ward's retirement, knocking out Vyacheslav Shabranskyy in the second round of a much-criticized title fight, and defended his title in March against little-known Igor Milhalkin.
Kovalev had a big fourth round, landing several powerful combinations and hard jabs that rattled Alvarez and slowed him. If he tastes his punch it could be lights out so he has to fight the ideal fight to come home with the belt.
But Kovalev collected himself and started throwing mean punches, seemingly taking over in the middle rounds with volume.
Bivol took it 116-112 on one scorecard, while two others had it 120-108, in convincing victory.
He was supposed to face unbeaten 2012 U.S. Olympian Marcus Browne, but when Browne ran into legal problems, Duva dropped him from the fight in April and secured an even more highly regarded opponent for Kovalev in Eleider "Storm" Alvarez, the long-avoided mandatory challenger for world champion Adonis Stevenson.