Nick Timoney's last-gasp try — his second of the contest — secured Ulster a crucial bonus point at Kingspan Stadium, although it will need to do the same again next week against Munster to qualify from Conference B.
Even then, a maximum haul may not be enough. Edinburgh, which faces Glasgow in the final round of fixtures, occupies third place and holds a four-point cushion over its nearest rival.
John Cooney scored 16 points, including grabbing the game's opening try, while Sean Reidy touched down in an impressive result for Ulster against the winner of Conference A.
In Sunday's (AEST) other fixture, Mattia Bellini scored a hat-trick of tries as Zebre made it back-to-back league wins with a 37-14 triumph over a much-changed Ospreys side.
The Italy international touched down twice in the space of three first-half minutes as Zebre raced out to a 22-0 lead.
Ospreys, which made 13 alterations from the team that lost 8-0 to Ulster last time out, finally got on the scoreboard 30 minutes in, Sam Cross touching down after a quick penalty.
Yet Bellini completed his treble after the hour as the Italian club comfortably held on to record a sixth win in the campaign, making this its best season in the competition.