Brentford went up to seventh in the Premier League table, heaping more pressure on bottom club Southampton with a comfortable win at the Gtech Community Stadium.
Ben Mee put the hosts in front, meeting Bryan Mbuemo's cross with a thumping header in the 41st minute.
And three minutes later Brentford doubled their lead after Mbuemo dispatched Yoane Wissa's cut-back into the bottom corner.
Mathias Jensen added a third nine minutes from time, nodding in a Rico Henry cross from close range.
With relegation rivals Everton edging out Arsenal and Wolves beating Liverpool, defeat left Southampton three points from a position of Premier League safety.
Meanwhile, Brentford extended their unbeaten run to nine matches, their longest in the top flight for 87 years.