Eoin Morgan is an England captain who senses his time has come. He has reshaped England's limited-overs cricket, now he wants some tangible reward for it. As the Champions Trophy looms, he is in mint form as his 11th ODI hundred in front of a near-capacity Headingley crowd testified.

Morgan's 107 from 93 balls was a central component of a victory that put England 1-0 up in the three-match series. He fell 14 balls from the end of the innings, advancing to Chris Morris, the most resilient member of South Africa's attack, and skying to mid-off. Along the way, he became the highest ODI run-getter of any batsman who has played for England, although that statistic is swollen by the 700-plus runs he made in an Ireland shirt. Ian Bell holds the record - as silky-smooth as he can be, already he feels like a batsman from another age.

South Africa, No. 1 in the ODI rankings, will provide an ideal pre-tournament workout for England, the hosts, ahead of the Champions Trophy. Morgan's third ODI hundred in eight hits, following two gained in the winter in Cuttack and North Sound, underlined that his game is in far better order than it was a year ago when his invigoration of England's one-day approach was not matched by his own form.

Even with Morgan's intervention, backed up by an inspired late assault by Moeen Ali which was enough to win him the man-of-the-match award on his return to the side, England had not quite put the game beyond South Africa at the interval. It was a record ODI score at Headingley, but it was a bountiful batting surface and, as evening approached, the day remained warm and the skies remained milky blue.

Nevertheless, England gradually imposed themselves in the field to secure a 72-run win. The luxury of that margin had seemed highly unlikely when South Africa were 145 for 1 approaching midway.

With the Manchester terrorist atrocity still so fresh in the mind, it was a pleasure to find Headingley carrying on regardless. The additional security was unobtrusive and, after a sombre minute's silence to start the day, and with both sides wearing black armbands, a crowd of more than 14,000 gradually slipped into contented mood. National security levels have been upgraded to Critical - the highest of the five categories, communicating the conclusion that another attack cannot be discounted - but there was no sense of a country under siege.

There will be disquiet at the fact that Ben Stokes was off the field for a period with a sore left knee, and only bowled two overs, but Morgan played down the significance of that and suggested that he was just being risk-averse. Anyway, if you worried every time an England player was off the field, you would rarely have time to do anything else.

Mark Wood has also had better nights. He touched 90mph at times, which is a good sign after his long-standing ankle problems, but too often he strained for rhythm, conceding 49 in his six overs. Hashim Amla pilfered five fours in two overs, easeful drives and pulls, and AB de Villiers looked equally commanding when Wood returned for a second spell.

All that was in the context of South Africa reaching 145 for 1 shortly before midway. Quinton de Kock fell early - a good running catch by the wicketkeeper, Jos Buttler, when he top-edged Chris Woakes - but Amla and Faf du Plessis had countered in inconspicuous fashion in a stand of 112. Then Wood trapped Amla lbw with a straight one - England winning the decision on review - Liam Plunkett straightened one to have du Plessis caught at the wicket in the next over and England rallied with Woakes snapping up the last two wickets to claim 4 for 38.

Self-destructive departures by JP Duminy and David Miller also played into England's hands. Both received long hops, from Adil Rashid and Woakes respectively, which they hauled obligingly to deep forward square. Moeen Ali found some purchase with his offspin and collected de Villiers to add to his earlier thumping 77 off 51 balls.

England's innings had provided the entertainment and, before Morgan's intervention, things were not quite so rosy. Stokes and Buttler were back from the IPL, their superstar status widely acknowledged, but there was no grand entrance as they returned to the England fold.

Stokes, named as the IPL's Most Valuable Player, as well as being the most expensive at $2.16m, looked in good order in making 25 from 30 balls before a meaty pull at a short ball from Kagiso Rabada picked out Morris at deep forward square. The boundary boards had been brought in at Headingley about five yards on that side of the ground, but that did not entirely prevent the conclusion - satisfying for local consumption - that they had clearly not been brought in as far as in IPL.

Buttler did not quite make the same impact in the IPL as Stokes, and he fell for 7 two overs later. Morris was brought back for him and the manner in which he immediately dismissed him at short backward square spoke of a pre-conceived plan.

After experiencing India's febrile crowds, an ODI in England had a gentler feel for Stokes and Buttler. They must have felt as if they were returning to suburbia after the clamour of the city (English cricket always feels like suburbia, especially at Lord's), the applause appreciative but not particularly noisy until Morgan and Moeen took hold in the closing overs. Politeness pervaded the scene.

Jason Roy departed early, driving expansively at Wayne Parnell's second ball to be caught at the wicket. By the time de Kock took his second catch, England had raised 100 at not far short of a run a ball. Alex Hales, who had worked the ball through the leg side confidently whenever given the opportunity, reached 61 before a lazy end against Andile Phehlukwayo's first ball. He normally feasts on width outside off stump but made a hash of it.

Joe Root lost impetus. The expectations of his home crowd were high in his first innings on this ground since his elevation to the Test captaincy. He got 17 off his first eight balls, but only 20 off his next 43 as Morris, not for the first time, restrained him best of all.

But it was Phehlukwayo who claimed his wicket. A seam bowling allrounder whose first sport as a youngster was hockey, he has no great pace, so there was little venom in his wide bouncer, but it was high enough for Root to get in a tangle as he tried to pull it and lobbed it into the leg side.

A partnership of 117 in 13 overs between Morgan and Moeen, who finished unbeaten on 77 with five sixes, replotted England's course. Moeen's contribution was also invaluable. He recovered from a careworn start by advancing to hit Parnell straight for six, and then clearing the ropes thrice more in an over from the legspinner Imran Tahir that cost 22. After the match, he said that England had dedicated the victory to all those who had suffered in the Manchester attack.