A 24-run victory in the first of five 50-over internationals followed a 2-0 win in the Twenty20 series after England had won the fourth and final match to complete a 3-1 triumph in the Test series.
Pakistan, who capitulated dismally in the second Twenty20 match in Cardiff, showed much more fight on Friday in a game reduced to 41 overs a side because of rain.
Chasing an impressive England score of 274 for six, they battled valiantly but lost wickets at important times to total 250 for nine.
Pakistan opener Kamran Akmal made an overdue return to form with 53 from 61 balls while his brother Umar hit 43 in 33 deliveries.
Slow bowlers Graeme Swann and Michael Yardy put a brake on the scoring after Pakistan had started brightly with 62 from 65 balls.
Swann struck yet again in his opening over and finished with two for 50 from eight while Yardy took for 49, also from eight.
Earlier, newcomer Davies anchored the England innings with 87 from 67 balls. He shared an opening partnership of 78 with captain Andrew Strauss, who struck two sixes in his 41.
Jonathan Trott added 69 before he became one of off-spinner Saeed Ajmal's four victims.
Test captain Salman Butt and pace bowlers Mohammad Amir and Mohammad Asif, who have been suspended after an investigation into incidents in the Lord's test, left for home on Friday.
They have agreed to fly back to England if police need any further help in a probe they are conducting into spot-fixing allegations.
The second one-day international is in Leeds on Sunday.
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