Hammers striker Javier Hernandez cancelled out Glenn Murray's opener before the break but the Seagulls struck back twice - first through Jose Izquierdo, then Pascal Gross - to claim all three points at the Falmer Stadium.
As a result, Brighton moved up to 13th in the Premier League standings and level on points with David Moyes's side, albeit still only three points above the dropzone in what is shaping up to be a 10-team relegation dogfight.
"We probably dropped our levels halfway through that first half - we were disappointed to go in at 1-1," Hughton told reporters at his post-match press conference. "Thankfully we got a very good reaction and the second half was as good as we've been in looking like scoring goals.
"That [second] goal lifted the stadium. Whatever goal gets us the lead is important but when it's as good as that it lifts everyone on the pitch and in the stadium. The most pleasing thing was that at 2-1 we could've been nervous and sat back on it but we didn't. We took that third chance and was a very big goal that releases any pressure we could've been under at the end.
"If we can put in more performances like this before the end of the season, then we'll be OK."
Next up for Brighton is a trip to relegation rivals Stoke City next weekend.