The result moves the Blues up to fifth.
Joao Pedro scored twice, while Jordan Henderson also grabbed an unlikely brace.
Earlier, Arsenal came from behind to get a 2-1 victory over Leeds, moving the champions level with Manchester City at the top of the table.
Brentford moved up to fourth in the table after a 2-all draw at Aston Villa.
Ipswich came from behind to beat winless Fulham 2-1 while Brighton won 2-nil away at Sunderland.
Tottenham moved off the bottom by grabbing a stoppage-time equaliser in a 1-all draw away to Manchester United in the late kick-off.
In League One AFC Wimbledon led leaders Plymouth before conceding a stoppage time goal to lose 2-1 at Home Park.
In the National League South Walton & Hersham made it back-to-back wins with a 1-nil victory at AFC Totton.
Hampton & Richmond Borough lost 2-nil to Ebbsfleet at the Beveree Stadium.
