Lauren Winfield (51), Heather Knight (53) and Natalie Sciver (51) all hit half-centuries as the tourists were bowled out for 295 in their 50 overs.
Sri Lanka, never in the hunt, were bowled out for 173 in 48.5 overs.
England join Australia in qualifying for the World Cup, which takes place in England in June and July next year.
The top four teams in the eight-team ICC Women’s Championship table qualify automatically, with the bottom four joining six other sides in a qualifying tournament, to be held in Sri Lanka early in 2017, to determine the final four World Cup qualifiers.
West Indies will become the third side to qualify automatically if they beat India on Sunday, while New Zealand and South Africa are battling for fourth place.
After Sri Lanka won the toss and elected to field, England made best use of the conditions at the R Premadasa Stadium as three of their top four passed 50, though none of them passed 53.
Captain Knight struck three sixes, while the free-scoring Sciver’s 51 came from only 27 balls.
When she fell, England were 198-5 in the 36th over – but while the lower order was occasionally prone to folding in their recent series in West Indies, this time Georgia Elwiss (46) and Danielle Hazell (29) marshalled the tail well, as the last five wickets added 97 in 15 overs.
It set up what would have been a record run chase for Sri Lanka, whose record ODI score of 282-5 against India at the 2013 World Cup was the only occasion on which they had made more than 251.
That never looked likely as off-spinners Hazell (3-38) and Laura Marsh (2-35) put the brakes on, five Sri Lankans were trapped lbw and two others run out as England cruised to victory, claimed a 2-0 lead in the series – and the two points to guarantee qualification.
Opener Tammy Beaumont donned the wicketkeeping gloves, which she had not done for England since 2011, as keeper Amy Jones was forced to miss the game through illness. (Courtesy BBC Sport)