Currently the REST APIs provide a way to pull 'last X results' (max 25) but there isn't a way to specify the last successful build. This is an issue if the last successful build was more than 25 builds ago.

Workaround:
An alternative would be to use the Pre/Post Plugin to label the successful builds and then call one of the following resources in order to filter what build numbers have the label:

• Build Service — Specific Project
• Build Service — All Builds