Noble marked his 200th appearance for the club with victory at Turf Moor as the Hammers managed to see out an early onslaught from the home side to triumph through goals from Diafra Sakho, Enner Valencia and Carlton Cole.
He told the club's official website: "I didn't even know it was my 200th Premier League appearance to be honest. But it's nice to reach it - it's a good marker when they're 38-game seasons.
"It's nice to get to 200 with a win too. It was important that we weathered their storm and stayed at 0-0 [at that stage], then come out for the second half and show our quality. We did that and deservedly got the win."
West Ham moved to fourth in the Premier League table courtesy of their win over the Clarets.