Jackson scored 15 points on the night with five penalties and that, combined with a try for the impressive Jared Payne, took Ulster to the top of the RaboDirect PRO12 table.
Munster flew out of the blocks early on and found themselves ahead after just three minutes as Ian Keatley was on target with a penalty from the right.
The 25-year-old fly-half was at it again just five minutes later, this time from the left, as Ulster buckled and conceded a penalty again.
And Keatley took his and Munster's points tally to nine on 12 minutes, shrewdly knocking over a drop-goal from close range to capitalise with his side camped in Ulster's half.
The hosts were shell-shocked but finally got onto the scoresheet on 16 minutes - 20-year-old fly-half Jackson, in for Niall O'Connor, making no mistake with a tricky effort from the right.
Jackson had a similar, if slightly harder effort, on 29 minutes as a couple of breaks from New Zealander Payne lifted the Ravenhill spirits, but the youngster struck the upright, leaving Munster 9-3 to the good.
Jackson did have the next say however, notching his second penalty but Munster then scored the first try of the match - a fine, flowing effort started and finished by replacement Keith Earls, on for the injured Luke O'Dea.
Earls made a break down the left and with Ulster struggling to get numbers back, the play was spread to the right through the hands of the impressive Casey Laulala and Doug Howlett to full-back Dennis Hurley, who fed back inside to Earls who cruised over - Keatley adding the extras.
But Jackson handed Ulster a lifeline in first-half stoppage time, knocking over another difficult penalty to leave the score 16-9 at the break.
Jackson continued to drag his side back into proceedings after the interval and he trimmed the deficit to four with his fourth penalty of the night and while Munster did their best to respond, Ulster's increase in intensity was soon to pay dividends.
After five minutes of concerted Ulster pressure, with Munster unable to get out of their own 22, it was Payne who finally found space to power his way across the line on 52 minutes but Jackson saw his conversion drift wide, leaving the hosts just a point ahead.
Munster hit back almost immediately with Hurley making a fine break but the wind was in Ulster's sails and a fine drive from the forwards resulted in Munster flanker Sean Dougall receiving a yellow card for illegally using his hands at a ruck on 57 minutes.
Replacement Craig Gilroy almost struck immediately but he was hauled down by Hurley just two metres from the line as Munster produced some superb last-ditch defence to keep Ulster at bay.
Whereas many in their position would have lost their heads, Munster kept theirs and despite feeding off scraps they remained composed when they got themselves up the field to set up Keatley for another drop goal on 66 minutes to retake the lead.
On 69 minutes, the lead swung back in favour of Ulster as Jackson showed nerves of steel to slot another penalty and while Munster huffed and puffed they couldn't find another way through as the hosts secured an impressive win.
|Ulster Rugby Score Card|
|Munster Rugby Score Card|