Rocked by the loss of three quick wickets against a side that has not beaten them in eight previous encounters, England staged a comeback through their fourth and sixth-wicket pairs in the Group A match at the Brabourne Stadium.
Struggling at 29 for three, Arran Brindle (31) and Heather Knight (38) steadied the England innings with a partnership of 64 for the fourth wicket in 100 balls.
After the loss of this duo in a span of overs, it was left to Jenny Gunn (52 off 71 balls) and Amy Jones (41) to carry on the good effort with a stand of 83 in 101 balls for the sixth wicket.
Later, the tail wagged as England added 59 runs in the last 30 deliveries, with Katherine Brunt making a quick 12 off five balls and Danielle Hazell chipping in with an unbeaten 19 of eight.
For Lanka, Kaushalya Lokusooriya, Chamani Senevirathne and captain Shashikala Siriwardene picked up two wickets apiece.
England lost their top three batters within half an hour after being put in to bat.
Captain Charlotte Edwards, playing in her fifth successive tournament, was bowled off the boots while attempting to hit a ball going down the leg off Kaushalya.
England dug themselves into a deeper hole when the other opener Danielle Wyatt, who too played a couple of spanking cover drives, and number 3 Lydia Greenway, were trapped leg before in successive overs by medium pacer Chamani.
The recovery act was staged by the right handed duo of Brindle and Knight before a run-out, following a misfiled, ended the blossoming stand. Chamani had a very fruitful five-over first spell of two for 18. More
