After taking the lead through a Charlie Hore penalty the Borders had gifted Ulster their first try Joe Pattison - who had come on for the injured Gareth Morton - wrongly thought the ball was trickling out of play after a chip ahead and eased up on the chase. However Paul Steinmetz was on hand to punish his error and give the visitors the advantage, Adam Larkin adding the conversion.
Although Ally Warnock narrowed the gap with a penalty the Borders were soon handicapped by the loss of Mark Blair to the sin bin - and in his absence Ulster extended their lead through a Bryn Cunningham try with Larkin again converting.
Larkin extended the lead further with two penalties before the interval - just as the Borders saw Kelly Brown dispatched to the sin bin.
However Warnock kicked the home side back into contention with two more penalties in the second half and although Jonny Weston bagged the late try, which Warnock converted it was just too little too late for the bottom side.
|The Borders Score Card|
|Ulster Rugby Score Card|