The Hammers edged into a slender lead after Mauro Zarate fired past Asmir Begovic from the edge of Chelsea area in the 17th minute of the derby at Upton Park.
England international Gary Cahill levelled just after half-time before Andy Carroll headed a late winner to secure three points and move the Hammers up to third place in the table.
West Ham centre-half Collins posted a photo of the dressing room celebrations on his Instagram page following their derby win.
Collins wrote on the photo-sharing app: “Another great 3 points….well done lads @whufc_official #coyi”
The Hammers have already beaten Arsenal, Chelsea, Liverpool and Manchester City in the Premier League this season.
The east London side have won six of their 10 league games so far this season and have only been beaten by Leicester City and Bournemouth.
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