Morgan (76) top-scored, and shared a fourth-wicket stand of 133 with James Taylor (60) – but otherwise, the tourists were off the pace throughout and undermined twice over by collapses.
They stumbled to 14-3 and then, on an increasingly sluggish surface, from 147 without further loss to 161-7.
In defence of a paltry 216 all out, even a fine new-ball burst by left-arm swing bowler Reece Topley, taking his first wickets in this format, and finished with 3-26, could not haul them back into the contest as Mohammad Hafeez (102no) and youngster Babar Azam (62no) eased Pakistan past their target in just 43.4 overs.
“Certainly we were slow out of the traps today,” said Morgan after his team had gone 1-0 down with three to play.
“Given the repair work James Taylor and I did, it’s very disappointing to lose two (more) in the space of four or five overs.”
During his century partnership with Taylor, Morgan was beginning to work out what a winning total might be.
“We were looking at a minimum 250 – but getting there, you can’t get ahead of yourself, particularly on this sort of wicket.
“It wasn’t a crash, bang, wallop type of wicket – I think we assessed that pretty quickly.
“After about 20 overs, the ball started to hold up and grip a little bit more.”
England’s bowlers were then left fighting a losing battle and, when asked if it might be an option to strengthen the attack, in the absence of injured all-rounder Ben Stokes, Morgan conceded that may be possible.
“Stokesy leaves a big hole – it’s something that we will look at,” added Morgan. “But I don’t think you can look into the bowling too much today - the batting let us down massively.”
Topley’s individual success was a minor consolation.
“He’s a big asset,” said the captain. “Long term, he’s certainly someone we’re looking to nurture. He’s very good for a 21-year-old.”
At the other end of the age spectrum is veteran Pakistan batsman Younus Khan, who caused a stir before play by announcing his 265th ODI would be his last.
Younus was a controversial inclusion for this series, having featured infrequently in recent months, and Pakistan Cricket Board chairman Shaharyar Khan did not sound especially enamoured in a television interview with his decision to pull out of the remaining matches.
But the 37-year-old said: “After the World Cup, I’ve been waiting for this moment for seven or eight months.
“I pushed myself, the selectors, everyone in Pakistan, that Younus Khan can still play one-day cricket for his country.
“It was never in my mind that I’d be playing two or three series.
“I just wanted one chance to play and retire myself, on my conditions.”
Pakistan’s all-time record Test run-scorer has no doubt his timing is spot on.
“I think this is the right time for me,” he added.
“My body is in good shape; my mind is in good shape, and my thinking is in good shape - so this is the right time.”
He will not be giving up Test cricket any time soon, though - with more than 9,100 runs to his name so far.
“I will try, at least 10,000,” said Younus.
“India have three or four guys who made 10,000 runs - and Sri Lanka, there is (Kumar) Sangakkara and Mahela (Jayawardene), they made it to 12,000.
“I will try ... until I get to 10,000 runs.”