After Matt Jarvis had broken the deadlock, Nolan, who had previously gone eight games without scoring, made sure of the points with an 80th-minute second that took his career tally to 100 in league matches.
He told reporters: "I've been getting the chances, but keepers have been making great saves. Thankfully it is done and dusted now.
"I'm just delighted to get it today and to get it when I did in the game, it took the pressure right off us."
The result moved the Hammers into the top half of the Premier League table and 11 points clear of the relegation zone.