Agha Salman (51 off 45 balls) was the only Pakistani batsman to score a half-century.
Playing his last match in England colours, David Willey (3/56) grabbed two early wickets to pin Pakistan back at the start of their chase.
A 53-run partnership for the last wicket between Haris Rauf (35 for 23) and Mohammad Wasim Jr (16 for 14) only delayed the inevitable.
First, Jonny Bairstow (31) and Dawid Malan (59) added 82 runs for the first wicket before all-tournament star Ben Stokes hit 84 runs from 76 balls with the help of 11 fours and two sixes.
Joe Root compiled a neat 60 off 72 balls. The pair of Stokes and Root put on 132 runs for the third wicket to power the defending champions, who will be returning home after this match. For Pakistan, Haris Rauf took three wickets for 64 runs while Shaheen Shah Afridi and Mohammad Wasim took two each.
England: 337/9 in 50 overs (Ben Stokes 84, Joe Root 60, Jonny Bairstow 59; Haris Rauf 3/64).
Pakistan: 244 all out in 43.3 overs (Agha Salman 51; David Willey 3/56).
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