England lost Alex Hales early on but were in a good position to take a 2-0 lead when rain terminated proceedings in the third ODI in Bristol. Sri Lanka had earlier posted an exceedingly gettable total of 248/9.
South Africa were knocked out of the Tri-Nation One-Day International series after suffering a heavy 100-run loss to West Indies at the Kensington Oval in Bridgetown, Barbados on Friday.
England easily eclipsed a decidedly average total from Sri Lanka to claim the first victory of the series and move into a 1-0 lead. Sri Lanka could only managed 254/7 which proved not to be a challenge as England's openers guided them to a ten wicket win.
Australia booked their berth in the final of this closely fought tri-series as they put together a very well-organised chase of 283 to beat the West Indies by six wickets in a compelling tussle in Barbados.
Near centuries from wicketkeeper-batsman Jos Buttler and all-rounder Chris Woakes saw England and Sri Lanka tie Tuesday's series opener at Trent Bridge in Nottingham.