Goals from Eden Hazard and Gary Cahill and a brace from Diego Costa took the hosts to within touching distance of the Premier League title.
Saints performed well in spells, but some pretty poor defending saw them concede four.
Oriol Romeu gave the visitors hope in the first half, levelling from Manolo Gabbiadini's pass after Hazard had fired the Blues ahead.
Antonio Conte's side then took the lead once more on the stroke of half-time, as Cahill headed home from Marcos Alonso's header back across goal.
Chelsea put the game to bed in the second period as Costa struck twice on 55 and 89 minutes.
Ryan Bertrand headed home a consolation goal for Saints late on from Cedric's right-sided cross.
Chief Photographer Stuart Martin was at Stamford Bridge - so be sure to check out the pictures above.
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