Keatley kicked a penalty for the visitors' first score on 18 minutes but Fijian wing Nagusa burst beyond the Connacht defence seconds later for another converted Ulster touchdown.
But Ulster were not to be denied and a minute after Cullen's heroics, Trimble found Steinmetz on a cutback run off the left wing and the Kiwi burst through to score under the posts and give David Humphreys a straightforward two-pointer.