Cook won the toss for the second time in the four-match series, then cashed in with 102, his fourth one-day century, from 118 deliveries in an England total of 250 for four.
Fast bowler Steven Finn then turned in another match-winning performance with four for 34 from 10 overs as Pakistan were dismissed for 230 from 49 overs.
Cook survived a chance on 30 to wicketkeeper Umar Akmal off Shahid Afridi during a technically assured innings against the spinners who had bowled their country to a 3-0 victory in the test series.
His opening partner Kevin Pietersen reached 26 in a partnership of 67 before he fell in familiar fashion, lbw to off-spinner Saeed Ajmal for 26.
Ravi Bopara compiled a second consecutive half-century with 58 and Eoin Morgan struck a brisk, unbeaten 25.
Mohammad Hafeez (26) and Imram Farhat (47) gave Pakistan a steady start with 61 but wickets then fell regularly as the England bowlers maintained a tight line and length.
Afridi struck 18 from as many deliveries and captain Misbah-ul-Haq kept his side in the hunt with 47 from 59 balls before he was brilliantly caught by wicketkeeper Craig Kieswetter, who clung on to a skied mis-hit at full stretch off Stuart Broad.
