Eradication of invasive species is difficult in the marine environment, and there have only been a few successes. We report the successful eradication of the invasive seaweed Undaria pinnatifida from a sunken trawler in the Chatham Islands, New Zealand. New heat-treatment methods were developed as the most cost effective and environmentally acceptable option to kill Undaria. Monitoring of the trawler for three years after it sank found no Undaria after the vessel was treated. Key factors in the success of the eradication programme included: early detection, a rapid response, pre-existing knowledge of Undaria, an adaptive management approach, targeting of multiple life history stages, and the cooperation of the vessel's insurer.