The Hammers were 1-0 winners at Upton Park on Saturday.
The Hammers were 1-0 winners over former manager Sam Allardyce on Saturday, as a goal from Michail Antonio sealed all three points for them.
It was not a wholly comfortable win for them though, with the Black Cats enjoying several chances to get something from the game themselves.
That was not a concern to West Ham co-owner Sullivan though; who says the nervous win shows that they are a good side.
“It was a close game against Sunderland that could have gone either way,” he told whufc.com.
“We took our chance and also hit the post twice. People could say we were lucky but we took our chances.”
“Over the season that is the difference between the good teams and the bad teams. The good teams manage to win a game like that and the bad teams don't.”
Slaven Bilic will now be hoping his side can enjoy similar good fortune for the remainder of the season.
They are very much in the hunt for a top six place this season, currently sitting 6th in the table, just a point behind Manchester United in 5th.
Crucially they are only four behind Manchester City in 4th, who do have a game in hand, a may even fancy a late push at qualifying for the Champions League with a strong finish to an impressive campaign.