With the Champions Trophy starting next week, tournament hosts England look in fine shape with bat and ball after a highly disciplined performance.
"It was very pleasing, it has been a pretty good day at the office for us," said Morgan.
"I thought the partnerships we built, we gave ourselves the best opportunity to get a par score or more," added Morgan, whose century was his 11th in ODIs.
England's spinning all-rounder Moeen Ali, who was given the man of the match award, struck a crucial unbeaten 77, including five sixes, in a match-winning 117 run partnership with Morgan.
Ali also played a key role with the ball, picking up the wicket of South African skipper AB de Villiers just as the strokemaker was beginning to look dangerous on 45.
The only concern for England was a knee injury for all-rounder Ben Stokes which hampered his ability with the ball.
BRIGHT START
The Yorkshire venue of Headingley welcomed the world's visiting number one ranked ODI team with bright sunshine before Morgan's 107 from 93 balls put the spine in England's total.
Ali's contribution was essential after the two strong-hitting middle order batsmen - Ben Stokes and Jos Buttler - had been dismissed for 25 and seven respectively.
Alex Hales (61) and local favourite Joe Root (37) had laid the foundations with a 98-run second wicket partnership after opener Jason Roy was caught behind for one by Quinton de Kock, attempting to drive Wayne Parnell.
South Africa made an excellent start in response, with Hashim Amla scoring 73 before he was trapped lbw by Mark Wood, departing at 145 for two.
Faf du Plessis, who had batted beautifully for his 67 in a 112 run partnership with Amla, quickly followed after edging Liam Plunkett with keeper Jos Buttler safely pocketing.
But, with England bowling a consistent and tight line and length, South Africa's middle order was unable to respond, De Villiers running out of partners before going on the attack and being caught by Plunkett at deep mid-wicket off Ali.
England seamer Chris Woakes did the bulk of the damage picking up 4-38.
The three-match series continues at the Ageas Bowl in Southampton on Saturday and finishes at Lord's on Monday.
(Reporting by Simon Evans; Editing by Ken Ferris)
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