Surrey opener Roy's quickfire 65 fired England towards an initial victory target of 261 yesterday.
But after a third and final rain interruption of this day/night fixture at 9:37 pm local time (2037 GMT), the umpires eventually called the game off with England 194 for three.
Eoin Morgan, the England captain, was 33 not out and Ben Stokes 15 not out.
Earlier, Pakistan were held to a modest 260 for six, captain Azhar Ali top-scoring with 82 after he won the toss.
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Pakistan were going well at 173 for three after 35 overs but then lost Azhar before a rain stoppage put a further break on their run-scoring.
Roy and Joe Root (61) took England to the brink of victory with a second-wicket stand of 89 in 14 overs.
Roy sparked England's chase with three fours in four balls off Umar Gul in the third over of the hosts' innings.
His boundary-rush started with a superb vertical bat shot through the legside.
Two balls later, Roy worked paceman Gul through long-on and the next delivery saw him force through the covers.
Meanwhile opening partner Alex Hales, who managed just 145 runs at during the preceding 2-2 drawn Test series against Pakistan, again fell cheaply.
Hales was out for seven when he guided Gul straight to Mohammad Hafeez at slip.
Mohammad Amir had had five catches dropped off his bowling during the Test series and the Pakistan paceman's bad luck continued Wednesday.
Roy, on 24, skied left-arm quick Amir high on the legside.
The ball appeared to be heading straight to Gul at square leg.
Pakistan may have recently climbed to the top of the Test rankings, but this was the kind of fielding error which had helped leave them languishing in ninth place in the equivalent ODI standings.
Roy swept left-arm spinner Imad Wasim for the first six of the match before completing a 43-ball fifty also featuring five fours.
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