Kumar Sangakkara made 115 in a Warwickshire total of 303-6 but a partnership of 223 between openers Phil Jaques (102) and Vik Solanki (144 n o) saw the New Road side past the total with eight wickets left and four overs to spare.
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Cov kid Ian Bell has kept his place in the England squad for the Third Test against the West Indies at Old Trafford.
Bell did not field during the two West Indies innings in the last test at Headingly due to back spasms but has recovered to stake his place in the side