England beat Pakistan to win one-day series
Success meant England had won consecutive Test (3-1), Twenty20 (2-0) and limited overs series against a Pakistan side whose tour was overshadowed by 'spot-fixing' allegations.
Man-of-the-match Morgan made 107 not out in a total of 256 for six after England had slumped to 47 for three following captain Andrew Strauss's decision to bat first.
Former Ireland left-hander Morgan had previously made an unbeaten 103 as England beat Australia by four wickets in the first one-dayer at the Rose Bowl in June.
Pakistan were eventually dismissed for 135 with 13 overs still left, seamer Stuart Broad taking three for 25 and off-spinner Graeme Swann three for 26.
"It was a huge game of cricket really, a very tough series," Strauss told reporters.
jaz Butt, the Pakistan Cricket Board chairman, fuelled the controversy engulfing this tour by accusing England of losing last week's third one-day international at The Oval deliberately.
"It's been a long summer and we've been to some pretty unpleasant places as a team over the last few days and had to show a lot of unity and togetherness," Strauss, the man-of-the-series, added.
"You could see how much it meant to us when the last wicket went down. Motivation wasn't a probem."
Pakistan captain Shahid Afridi said: "I was thinking about a happy ending but it hasn't happened.
"There were some controversies on this tour but my team was very united and I think this will give us some good results in the future."
Shoaib Akhtar, in what could be the 35-year-old Pakistan fast bowler's last international in England, gave fans something to remember him by with three wickets for 40 runs, including an impressive opening spell of two for 17 in six blistering overs.
Pakistan, who had been 2-0 down in this series, saw openers Kamran Akmal and Mohammad Hafeez put on fifty in just 47 balls featuring 10 boundaries.
But Broad took two wickets in two balls to leave Pakistan 63 for two.
Hafeez went for 29, courtesy of the latest brilliant backward point catch by Paul Collingwood and Broad then had Asad Shafiq caught behind by wicketkeeper Steven Davies.
Mohammad Yousuf survived the seamer's hat-trick but England had regained control of the match.
England then had a massive slice of luck when Kamran Akmal was given out lbw for 41 to medium-pacer Luke Wright by home umpire Ian Gould, despite edging onto his pad.
Swann, whose fifth delivery had seen Fawad Alam bowled in classic style, struck twice in two balls to remove Yousuf and Afridi - like Asif out for a first ball nought - to leave the tourists all but beaten at 104 for six.
Earlier, Morgan had a reprieve when on 31 he chipped off-spinner Hafeez down the ground and Yousuf held a fine catch over his shoulder.
But Yousuf, realising he could not stop himself from going over the boundary, threw the ball in-field to prevent a four only to turn his ankle as he slipped in the process, an injury that later meant he batted with a runner.
Morgan, on 91 when the last over started, struck off-spinner Saeed Ajmal straight for six and four off successive balls to complete a 97-ball century.
Jonathan Trott, whose pre-match confrontation with Wahab Riaz ahead of the tourists' victory at Lord's on Monday had fanned the flames of the 'fixing' controversy, walked out to a chorus of jeers.
And it wasn't long before Trott, cheered by England supporters as much as he was booed all match by Pakistan fans, was out for three after Akhtar's express off-cutter demolished his stumps.
Pakistan's Salman Butt, Mohammad Aamer and Mohammad Asif have all been suspended by the International Cricket Council and questioned by British police over an alleged plot to bowl deliberate no-balls during last month's Test at Lord's.
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