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.
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.