Zimbabwe's nine-wicket defeat by Group A winners India on Monday ensured Ireland's place in the top three.
The Irish lost to India and hosts Sri Lanka but beat Zimbabwe and Thailand.
Ireland retain their one-day international status by making the Super Six, from which the top four qualify for the World Cup this summer.
Sri Lanka finished second in the group while tournament favourites India boasted a 100% record from their four games.
Ireland are are also joined in the Super Sixes by South Africa, Pakistan and Bangladesh.
Their next game is on Wednesday when they face Bangladesh, before taking on Pakistan on Friday and South Africa two days later.
Zimbabwe required a victory over India in Colombo, along with a significant improvement to their net run rate, to overtake Ireland and make the last six.
Ireland completed their group matches on Saturday with a 46-run win against Thailand, who ended bottom of the group.
Kim Garth hit an impressive 98 and Laura Delany added 50 while seamer Lucy O'Reilly took 3-28.
All matches played in Colombo & start at 04:30 GMT. CCC = Colombo Cricket Club; MCA = Mercantile Cricket Association Ground; NCC = Nondescripts Cricket Club; PSS = P Sara Oval
Ireland have progressed to the Super Six stage of the Women's World Cup Qualifier after finishing third in their group in Sri Lanka.