Frank Lampard gave the visitors the lead in the first half after he finished a Ramires cross before the hosts struck back after 36 minutes through Vicente.
An error from Raul Meireles let in Will Buckley and although Petr Cech saved his effort, Ashley Barnes was on hand to put the south-coast side a goal up, before Andrew Crofts sealed the victory late in the second half as the Blues slipped to their third defeat of pre-season.
West Brom needed a late equaliser from Peter Odemwingie to salvage a 1-1 draw at Sheffield Wednesday.
The hosts took the lead through Nejc Pecnik after 34 minutes with a cross-cum-shot which looped over Ben Foster before the Nigerian international scored in the 88th minute.
Championship side Nottingham Forest recorded a 3-1 win over top tier club Aston Villa at the City Ground.
After a goalless first half, Lewis McGugan netted from the edge of the area after 71 minutes to put the home side in front before captain for the day Barry Bannan equalised for Villa with a free-kick two minutes later.
Marcus Tudgay was on target after 77 minutes to put Forest back in front before McGugan rounded off the scoring with five minutes left.
Premier League newcomers Reading drew 2-2 at Bournemouth.
Adrian Mariappa headed home a Nicky Shorey free-kick before the Cherries equalised through Wes Thomas, who converted a Matt Tubbs cross.
Hal Robson-Kanu put the visitors in front from the penalty spot but Miles Addison rescued a draw for the home side.
West Ham, who before Saturday's match at Ipswich had already lost three pre-season friendlies, fell behind after 15 minutes when Michael Chopra netted from the spot.
Summer signing from Nottingham Forest Luke Chambers put the hosts two goals up four minutes later with a header.
Matt Taylor pulled one back for the visitors after 73 minutes with a long range effort, but Jason Scotland sealed a 3-1 win for the Suffolk side seven minutes from time.
And the other Premier League new boys, Southampton, beat last season's top flight basement boys Wolves 2-0 at St Mary's.
Saints took a first half lead when Billy Sharp converted an Adam Lallana cross for his fourth goal of pre-season, before Jason Puncheon doubled the lead midway through the second half when he drove into the net from the edge of the area.
Sunderland followed up a 1-0 pre-season defeat to Hartlepool with a 2-0 reverse against Helsingborgs in Sweden.
After a goalless first half the hosts took the lead after Alfreo Finnbogason's strike hit the post then rebounded off goalkeeper Simon Mignolet and into the net.
The lead was doubled after 73 minutes when a low strike eight yards out by May Mahlangu went under the Belgian.
North-east rivals Newcastle faired better as they drew 0-0 with Dutch side ADO Den Haag.
Gabriel Obertan was unlucky not to find the net with a dipping volley after 24 minutes which was well saved by home stopper Gino Coutinho, while Shola Ameobi had a goal ruled out for offside after 79 minutes.
Mladen Petric opened the scoring as Fulham enjoyed a 4-0 victory over Nice in their friendly at the Stade Municipal du Ray.
Petric scored after 18 minutes before turning provider to release Alex Kacaniklic just before half-time to double the advantage.
Petric again provided the pass for Mahamadou Diarra on 64 minutes before substitute Mesca, who had been on the pitch only two minutes, added a fourth 11 minutes from time.
