Welshman Ramsey, against his former club, opened up the scoring just before the half-hour mark with a stunning header from a fierce Mesut Ozil cross from the left before Flamini added a second four minutes from time when he rifled home Ozil's clever through ball from inside the area.
Jay Rodriguez gave the Saints an early lead when he pounced on a poor backpass from Michael Essien to slot home in just the 13th second but the Blues rallied with three second half-goals to record a second straight win.
Gary Cahill nodded home in the 55th minute in a goalmouth scramble before John Terry marked his 400th league appearance with a glancing header from Juan Mata's leftwing cross prior to Demba Ba adding a third in the final minute.
In other key matches, Manchester United twice came from behind to force a 2-2 draw thanks to a Wayne Rooney double, Hull City shocked Liverpool 3-1 at home, Everton dominated Stoke City to win 4-0 and Newcastle United moved up to sixth courtesy of a 2-1 victory over West Bromwich Albion.
Fulham suffered a fifth straight defeat when losing 3-0 to West Ham United at Upton Park, which ultimately cost manager Martin Jol his job, Norwich City edged Crystal Palace 1-0 and Aston Villa and Sunderland played out a 0-0 draw.
The next Premier League fixtures take place on Tuesday, December 3 with Palace hosting the Hammers before a full schedule of matches on Wednesday which includes Everton's trip to Old Trafford, Fulham's clash with London rivals Tottenham and Arsenal's home meeting with Hull.
2013/14 Barclays Premier League - season scores
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