Duckett's career-best 167 off 132 balls on Thursday propelled England to 5-386 — the highest-ever ODI score at the Gaddafi Stadium in Lahore — after Kusal Mendis won his seventh successive toss on the tour and elected to field.
Pavan Rathnayake then followed his century in Sri Lanka's astonishing run-chase against England at Rawalpindi last week with 118 off 77 balls before falling to Dawson in the 45th over as Sri Lanka got bowled out for 331.
It was England's first ODI win in Pakistan since 2005 after they lost their first three games in this tri-series to put themselves out of the running to make Saturday's final.
Last week, England captain Harry Brook's fastest-ever ODI double-century wasn't enough to stop Sri Lanka from successfully chasing down the second highest-ever total of 430 in the 50-over format.
England also crashed to an 87-run defeat in their opening match against Pakistan.
Rathnayake's third ODI century against England this year kept Sri Lanka in the hunt for another big chase in the tournament after Mendis hadf opted to field for the fourth consecutive time.
Mendis made 89 off 71 balls and rebuilt the chase with an 84-run second-wicket stand with Avishka Fernando, who scored 48, after Kamindu Mendis was clean bowled by Sonny Baker in the fourth over for four.
Part-time offspinner Joe Root got Mendis to give a faint edge behind while trying to sweep but Rathnayake then took charge and hit 15 fours and a six before miscuing a sweep against left-arm spinner Dawson and top-edged to fine leg.
England claimed the last three wickets for three runs for their first win.
Earlier Duckett's sixth ODI hundred and Tom Banton's 74 off 75 balls gave England a strong platform with a 163-run opening stand in 25 overs.
Brook, made 44 and put on another brisk 107 off 75 balls with Duckett as they carried England to 2-270 in the 38th over.
Duckett surpassed his previous ODI best of 165 made against Australia at the same Gaddafi Stadium during the Champions Trophy last year, having completed his century off 89 balls.
Will Jacks made 30 off 21 balls while Jordon Cox scored 43 off 27 balls and Sam Curran was unbeaten on 21 as England finished strongly after Duckett's dismissal.
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