Both action=edit and prop=revisions support sections. But, you have to use the section number, and there's no easy way to get it, besides parsing the wikitext yourself or doing something like http://en.wikipedia.org/w/api.php?action=parse&text={{:Page}}__TOC__&prop=sections
(the "TOC" is necessary because action=parse won't give the sections if there are less than 4, unless that's preset)
Ideally there should be some way to get the section number given only the page title or id, and the section name, or alternately, modules that allow sections should accept a section name.
Version: 1.14.x
Severity: enhancement