Rickie Lambert's 35th-minute free-kick proved enough to seal a 2-1 win at St Mary's after an early opener from Jay Rodriguez had been cancelled out by a header from John Terry.
Chelsea's shock loss allowed Tottenham to leapfrog into third place with a 2-1 win at Swansea.
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The latest weather update for the east with Philippa
The latest weather update for the west with Philippa
Philippa has Saturday's weather for the east