Eden Hazard and Diego Costa scored the goals to lift Antonio Conte’s side to fourth, one point behind Manchester City, Arsenal and Liverpool at the top.
Hazard, who caused Southampton problems throughout the Sunday encounter, opened the scoring after just six minutes and Costa, with his 40th goal in 66 appearances, sealed the victory.
Southampton remain ninth after what was their first league home defeat of the season.
In the day’s other match, Romelu Lukaku and Ross Barkley scored as Everton beat West Ham 2-0 to consolidate their top-six spot.
The result moves the Toffees to within two points of Tottenham, who fell to fifth after Chelsea’s victory.
West Ham remain just two places above the relegation zone.
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