The striker scored the opening goal with a powerful early header and a second from Mohamed Diame put the Hammers clear.
Adam Johnson's strike gave Sunderland hope but they were unable to earn anything from the match as their own survival hopes suffered a major blow.
West Ham now have 37 points, are comfortable in mid-table, and Carroll echoed co-chairman David Gold's Twitter claim that they are out of trouble.
"You take every game as it is, keep an eye on the teams winning below, but I think we are safe, yeah," he told Sky Sports 1.
Carroll's man-of-the-match performance again roused the debate as to whether or not he should be picked for the World Cup.
"That's what I'm looking for now, scoring goals and keeping on it until the end of the season," he added.
Captain Kevin Nolan was pleased to win at a side who were looking to reel West Ham back into the relegation fight.
"We knew it was going to be tough and Adam Johnson made an impact. We knew it would not be easy because they're scrapping, but we knew if we won we'd be clear of them," he said.
"We got the three points and put space between us and the bottom three."