He dropped Kovalev three times in a brutal seventh round and won the 175-pound championship by knockout at Hard Rock Hotel and Casino on Saturday night.
Kovalev (32-3-1, 28 KOs) was dominating his Colombian adversary early and often and appeared to be well on his way toward victory.
Alvarez (23-0, 11 KOs), 34, a Colombia native who lives in Montreal, earned a shot at Stevenson by virtue of his majority decision win over Chilemba in 2015, but for reasons never made clear, he never got the chance to fight Stevenson.
"Words can not describe how I feel", Alvarez said through a translator. Badly hurt, Kovalev got up, but went down again when Alvarez exploded with a left-right combination.
After the fight, Kovalev was taken to the hospital to get checked out.
"We slowed him a bit and I felt his punches weren't as hard as they were at the beginning of the fight", Alvarez said. I feel OK. Thank you everyone, thank you very much to all the fans around the world for your support. Eleider Alvarez has been out of the ring for almost a year, but is the Colombian ready to face off against this confidence-stricken version of Kovalev?
Vadim Kornilov, Manager of Dmitry Bivol, said the WBA champion is hoping for a unification fight before the end of the year, possibly against Alvarez. He's only fought once since then and really isn't ready for someone of Collazo's class with just 16 fights into his career.
"I was very happy with how the fight was going but I kept saying to (Kovalev manager) Egis (Klimas), 'Let's get past the sixth round and I'll relax.' But you saw what happened".
Despite Alvarez not being a big puncher, Kovalev knows that he's in for a tough fight.
He knocked Kovalev down twice and then finished him off with consecutive right hooks to the head that sent him down for the third and final time. Alvarez is an unbeaten prospect, who has bided his time - and often been forced into that by the WBC - taking in all that has taken place around him as he has patiently waited for his opportunity.
Kovalev had a big fourth round, landing several powerful combinations and hard jabs that rattled Alvarez and slowed him.
Kovalev was being lined up for a unification fight with 175-pound world titleholder Dmitry Bivol (14-0, 11 KOs), 27, of Russian Federation, in December.
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. But when that fight was delayed time and again, he quickly accepted the fight with Kovalev when it was surprisingly offered. The fight with Chilemba was Bivol's third in his past four bouts to come on a Kovalev undercard, as their seemingly inevitable showdown drew closer until the shocker in the main event.
Scores of 120-108, 120-108 and 116-112 went in favour of the incumbent, whose strong performance in the first six rounds helped him to weather a late rally from the Malawian.