Nat Sciver (77) and Danielle Hazell (45) helped England recover from 58-6 to post 240-9 on Thursday before rain forced the game into a reserve day.
Laura Marsh took 4-21, including her 100th ODI wicket, and Hazell 3-21 as Sri Lanka were bowled out for 78.
England secured qualification for the 2017 World Cup in the second ODI.
"It was nice, in the face of a potential collapse, to turn it around and win," captain Heather Knight said.
"We've had a really good year and I think the girls are really starting to take responsibility and grow into their roles."
New Zealand guaranteed World Cup qualification with a seven-wicket defeat of Pakistan in Nelson on Thursday - joining Australia and England in next year's tournament, which will be held in England in June and July.
The fourth and final automatic place is between West Indies and India - and will depend on how the International Cricket Council rules on an unplayed series.
With every team expected to play each other over a two-year period, a scheduled series between Pakistan and India - due to take place before the end of October - did not happen, and looks unlikely to do so for political reasons.
If the six available points from that series are shared, fourth-placed West Indies would finish above India as they have recorded the most wins of the pair.
The Windies would also stay fourth if Pakistan, as the home side, are awarded the points because of the Indian board's perceived reluctance to play them.
The fifth-placed side will join South Africa, Pakistan, Sri Lanka and six other teams in Sri Lanka early next year, to play a final qualifier for the last four places in the World Cup.

Pearson, 33, began his career at Motherwell before leaving to join Celtic in 2004.
He returned for a second stint at Fir Park in 2015 after spells in England with Derby, Stoke and Bristol City.
"This was something I was really keen to do and I want to thank everyone at Motherwell for the way they've handled this," Pearson said.
"It's with a heavy heart that I go, but at the same time, I am confident the club is in decent shape, with a very good manager and some exciting young talent bubbling under the surface waiting to get their chance, alongside the excellent senior professionals already there.
"I've enjoyed my second spell at Fir Park. I want to thank the fans for all their support and who knows, one day I may be back for another go at it."
Pearson was under contract with Motherwell until October and the Lanarkshire club have received compensation from Atletico de Kolkata.
Motherwell manager Mark McGhee said: "We are desperately disappointed to lose Stephen, but we've known for some time now that this move was on the cards.
"There was absolutely no fall out, it was all extremely amicable, and we understand his personal circumstances. He leaves with the best wishes of everyone at Motherwell FC.
"However, it was then incumbent upon us to try and recoup something to help us find someone else, and that's what we've done. We have been and are engaged in trying to secure a replacement and the midfield area is our priority."
Meanwhile, defender Steven Hammell, Motherwell's post-war record league appearance holder with 530 games, has agreed a new two-year contract.
He said: "I've never made any secret of my feelings for this club, so there is no one happier that my future is sorted out and I can get on with my football."
England completed a 4-0 women's one-day international series whitewash as they thrashed Sri Lanka by 162 runs in the final match in Colombo.
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Motherwell midfielder Stephen Pearson has left the club to join Indian Super League side Atletico de Kolkata.