Goals either side of the break from Andy Carroll and Mohamed Diame had the Hammers in pole position at the Stadium of Light before Adam Johnson's 65th-minute effort sent some scares through the east Londoners.
However, West Ham got the job done to remain 11th on the table - now 11 points clear of the relegation zone - and closing in on Stoke City in 10th which delighted Nolan.
"We knew obviously that it was going to be tough tonight but we dealt with them well," he told Sky Sports.
"I thought Adam Johnson made a great impact when he come on. It was a fantastic goal but we were quite comfortable throughout the game.
"You get no easy games, especially when they are scrapping for their lives. We knew if we won the game we would go 12 points ahead of them which is massive. So it was bigger for them than us.
"It was about us coming here with a game plan and the game plan worked a treat and we got the three points away.
"It puts a bit more space between us and the bottom three now and we are looking up to Stoke and trying to get into that 10th position."
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