Edinburgh impressed in spells but their indiscipline was their undoing, ensuring their impressive run of four wins in five matches came to a halt - head coach Alan Solomons seeing his former side get one over his current outfit.
Edinburgh began brightly and the Murrayfield faithful were on their feet early on after Dougie Fife raced down the wing, only to be forced into touch short of the try-line.
That didn't knock the wind out of the hosts' sails however and the impressive Bezuidenhout notched a superb penalty on 15 minutes to break the deadlock.
Ulster were struggling three minutes later when Iain Henderson was sent to the sin bin for a dangerous tackle, although Bezuidenhout was wayward with the resulting penalty.
It seemed to stir Ulster into life however and after keeping things simple while a man down, Ulster were awarded a penalty on 23 minutes after Edinburgh were pinged for coming into a maul at the side.
Jackson made no mistake from the tee to level the scores and on 36 minutes the Ireland fly-half kicked Ulster into a 6-3 lead after Edinburgh were penalised at a scrum.
He had another effort two minutes before half-time - this time the penalty awarded for obstruction - but he couldn't find the target and Edinburgh pressed in the closing stages, only to be pinged on the Ulster 22, ensuring they went into the break three points down.
After the break Edinburgh found that their indiscipline was letting them down again and after another penalty from a scrum on 46 minutes, Jackson further extended Ulster's lead.
Edinburgh then enjoyed some promising possession but they found Ulster in uncompromising mood and the visitors began to exert a stranglehold on the game.
The hosts responded however and with 12 minutes to go they threatened the first try of the match, only for a knock-on to cost them dear after good work from Harry Leonard and Josh Strauss.
With seven minutes to go Jackson attempted a drop goal to give Ulster the cushion they were after but his effort drifted wide, ensuring a tense finish.
Edinburgh threatened with four minutes to go but Ulster forced a superb turnover on the half-way line but again the hosts kept pushing, only for their discipline to let them down again - conceding a penalty at the breakdown near the visitors' 22.
And that was as close as they came as Ulster held out for a valuable victory in the race for the RaboDirect PRO12 play-offs.
|Edinburgh Rugby Score Card|
|Ulster Rugby Score Card|