Jackson slotted two penalties in the first half and one in the second to one first-half strike by Carl Bezuidenhout, to leave Edinburgh with only a losing bonus point and Ulster with four points which lifted them to second spot.
The rain hammered down in the opening quarter as Edinburgh hammered on the visitors' line, but the pressure was easily absorbed by the Ulster defence.
Grayson Hart and Dougie Fife came closest but finally a penalty, the first of many in the first half, allowed Ulster to clear.
The conditions were never going to allow flowing rugby and it was inevitable that the first points came from a penalty as a monster kick from Edinburgh number 10 Bezuidenhouit from halfway cleared the bar to take the home side into the lead after 14 minutes.
Ulster were having trouble with the sparky Edinburgh backs and their task became no easier after lock Iain Henderson collected a yellow card on 20 minutes, but Edinburgh were unable to take advantage.
Despite being a man short, Ulster muscled their way into kickable territory and, when Edinburgh again offended, Jackson had no difficulty in levelling the scores.
The game then developed into a midfield struggle with neither side getting the upper hand, but Edinburgh found themselves consistently frustrated with any momentum they tried to build hindered by giving away frequent penalties.
With seven minutes left in the half, Jackson again had the chance to slot a penalty and his kick was good to give Ulster the lead.
That advantage was almost increased by a third Jackson penalty attempt soon after but it fell just short.
Ulster went in 6-3 up having visited the Edinburgh 22 no more than three times, and the frustration was easy to see on the home faces.
The visitors started the second half at a fair lick with Henderson, John Afoa and Roger Wilson taking play into he Edinburgh 22 and, from the almost inevitable offence, Jackson added penalty number three to put Ulster 9-3 ahead.
The second half now replicated the first except that it was Ulster who dominated possession and territory with Edinburgh having to defend against remorseless attacks.
They withstood everything Ulster grew at them, however, with Roddy Grant, Cornell du Preeze and Grant Gilchrist performing heroically in defence.
The only respite came when, from a turnover, Nick De Luca slammed the ball deep into Ulster territory but the ball was eventually scrambled away.
As the final whistle loomed, Edinburgh finally strung some passes together, but they were forced to play too much rugby too far from the red zone.
And, to the surprise of no-one, a match which was dominated by the miserable conditions ended with Ulster kicking a penalty into touch.
- Sports & Recreation