Equivalent expressive power does not necessarily mean identical interfaces.
Structured query is primarily intended for use with the REST, Java, and Node.js Client APIs. Use the Node.js Client API queryBuilder interface to construct a structured query. See http://docs.marklogic.com/guide/node-dev/search#id_28266.
Alternatively, if you do not want to use the builder for some reason, you can roll your own combined query that contains a structured query. See http://docs.marklogic.com/guide/node-dev/search#id_57610.
On the server side, the recommended search API for JS is jsearch. See http://docs.marklogic.com/js/jsearch and http://docs.marklogic.com/guide/search-dev/javascript#chapter. Jsearch operates on cts:queries. Structured query is really just a thin layer over cts:query.
It is possible to call search:resolve (as search.resolve) from JS, just like any other XQuery library, but it is XML-centric, so it is not very convenient to use it from JS.