Even though it looked to this writer that he was losing nearly as many rounds as he was winning, Ward's body attack took a brutal toll on his Russian nemesis.
Weeks jumped in and waved off the fight at 2 minutes, 29 seconds.
"I knew this time it was going to be different", Ward said.
On the Ward vs. Kovalev undercard, unbeaten Cuban gold medal Olympian and WBA super bantamweight champion Guillermo Rigondeaux (17-0, 11 KOs) returns the boxing ring, and will take on fellow unbeaten fighter Moises "Chucky" Flores (25-0, 17 KOs). Their records are nearly identical and both fight with a great deal of intelligence.
Ward won the first fight in November, coming back from a second round knockdown to get a controversial decision.
'It's more like it's a dream, ' Ward said.
"I told [the media] this week I have only trained Andre for a knockout twice", Hunter said.
Ward and his camp dismissed any idea that low blows were a factor, preferring instead to celebrate a win that put to rest any controversy over the judging in their first fight last November.
"I don't have anything on the books right now for a cruiserweight fight, a heavyweight fight". The Russian - and many ringside observers - were surprised that Kovalev lost the first fight.
For Andre Ward stopped the frightening Sergey Kovalev...with body blows in the eighth round. "I knew I had about 30 seconds to go in the round and I just had to finish it. I wasn't hurt and I could continue".
Ward was up by a point on two scorecards and down three points on the third going into the eighth.
'Kovalev also was probably up in the fight, at least by a little bit. Ward's final flurry included several borderline shots and Weeks should have given Kovalev a standing count rather than waved it off. Ward threw and landed fewer punches than Kovalev but hit 37 percent of his power shots, according to Compubox. "I thought I was doing very good". I see things with him in particular and he's the best.
Ward replied, "You got me sweating".
"When he can't get you out of there he fades", Ward said.
There was genuine dislike between the two fighters, born largely out of their first fight. I didn't predict a knockout, but I said it could happen.
The American boxer, 33, wanted to stamp his authority on rival Sergey Kovalev on Saturday night and said in the build up he wanted to stop him. If he doesn't, Ward is going to out-box him over 12 rounds and win a decision about which no one can complain.
Ward, who is promoted by American rapper Jay Z's nascent Roc Nation Sports, has been guaranteed a minimum purse of US$6 million (S$8.2 million).
The victory was disputed as television replays showed Rigondeaux landed a left hand after the round-ending bell had rang.