James McClean put the hosts ahead early on and they wrapped up three crucial points with further efforts from Steven Fletcher and Stephane Sessegnon.
O'Neill said: "I am delighted to have won, naturally, and there's a sense of relief too that we have done that. It was good to win the game."
The win lifted spirits at the Stadium of Light enormously ahead of a difficult run of fixtures including Saturday's trip to Manchester United and a visit to Southampton before champions Manchester City head for Wearside.
He said: "It's the winning of football games. It doesn't matter about performances.
"We had a really excellent second-half performance against Norwich which yielded nothing - although you might say in the first half, we probably didn't deserve it - and we showed a lot of commitment against Chelsea here.
"But you can talk until you are blue in the face, you have to win some football matches, and it's definitely just a great old feeling.
"Of course, we have got tough times ahead at this minute, far from anything being clear.
"It might have lifted us a couple of places in the league, but it's the points on the board that are essential, and we have got a really tough time between now and New Year.
"We will just have to try to see it through if we can, but that was a boost tonight anyway for us."
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- Manchester United