Marcus Trescothick quickly became frustrated, lofting Vaas to mid-on one ball after inside-edging an ambitious pull shot to the fine-leg fence, England's last boundary for 31 overs.
But Collingwood chipped in with the key wicket of Chanderpaul, who top-edged a pull straight to substitute fielder Ian Bell at deep square-leg and the requirement was 104 from 89 balls with only six wickets remaining.
The recalled left-hander smashed eight fours and a six in a valuable knock before a mis-timed pull off the otherwise expensive Finn presented Anderson with a straightforward catch at square-leg.
Tamim was quiet for a while, but then stepped up several gears, hitting three boundaries in a row off Finn, a lucky edge just past gully sandwiched by a clumping on-drive and a terrific pull off one leg.
But Belgium's Xavier Malisse was forced to pull out of the eight-man round-robin tournament after retiring with a leg injury against Frenchman Sebastien Grosjean .