The world champion, who won all three titles from the Russian by a controversial points decision in their first bout, is unbeaten in 32 fights.
The American wobbled Kovalev with a right hand in the eighth and finished him off with a series of body shots.
Kovalev said he was hit by a low blow, adding that he wanted another rematch.
"He's a great fighter, not a lot of people are going to beat him," said 33-year-old Ward, who has 16 knockouts from his 32 bouts.
"But when you are facing a great fighter you have to raise your game to the next level.
"I hurt him with a head shot and I just had to get the right shot in to finish him."
Kovalev started strongly before Ward came back into the fight at the Mandalay Bay Hotel.
Referee Tony Weeks then stopped the fight with 31 seconds in the eighth with Kovalev, 34, kneeling down.
"It was a low blow, again another one," said Kovalev.
"We are boxers. I could still continue. Why stop the fight?"

The agency said almost 20 hectares of forest would have to be felled to try to stop the disease spreading.
Phytophthora ramorum is a fungus-like pathogen that can kill or severely damage larch trees.
Forest Enterprise Scotland (FES) is also asking woodland visitors to help prevent the spread of tree disease.
It called on people to brush mud and forest debris from boots, walking poles and bike tyres when leaving and entering wooded areas.
All the new sites are close to existing infected sites.
FES confirmed the locations as:
Fraser McDonald, a forester with the FES team in Cowal said: "Everyone has a part to play in helping prevent the spread of tree diseases and it's simply a matter of making sure that you arrive at a forest with clean boots, bike wheels - and even dog's paws.
"Our Keep it Clean campaign promotes good biosecurity practice and explains that it only takes a few minutes to brush off any mud or forest debris from boots, walking poles or bike tyres.
"It may not seem much but tree diseases can be carried from site to site in mud or on twigs leaves and others forest debris, so those few minutes can make a big difference."
Mr McDonald said Scotland's forestry was a valuable resource for recreation and the economy of Scotland.
He added: "It's important that everyone does there bit to look after Scotland's forests and help to prevent the spread of tree diseases."
Andre Ward stopped Sergey Kovalev in the eighth round to win their light-heavyweight rematch in Las Vegas and retain his WBO, WBA and IBF belts.
[NEXT_CONCEPT]
A deadly pathogen that kills larch trees has been discovered in seven new locations across Argyll and Stirling, Forest Enterprise Scotland has warned.