"He scored two very important goals for us and hopefully he'll keep scoring goals for us," said the former Chelsea forward.
"There's so much speculation but, as far as I'm concerned, he's our player. It's as simple as that.
"He's a very important player and is enjoying a very good moment.
"The club knows I don't want to sell Bellamy and we have had a total understanding right from the start.
"With all the talking around him, another player might have been affected. But he's a professional and is very good. Everything he does is spot on.
"For me, I think he can be even better than he was today."
Jack Collison and Carlton Cole also scored in the much-needed victory, which was only the second in 13 league games for the Hammers.
Having been a point and a place above the relegation zone heading into this fixture, Zola was delighted with three vital points.
"It was fantastic," he said. "We deserved to win today, even though it was a very close game.
"They were very close to winning as well but, fortunately, it went our way."