After a rather lacklustre start Ulster were soon in the ascendency against their Italian opposition and a great score from Darren Cave alongside Jackson's accurate kicking made sure of a second straight RaboDirect PRO12 victory.
The Ulster scrum were getting the better of the earlier exchanges, driving their Italian opponents back at every opportunity, but in the tenth minute Zebre were awarded a penalty at the scrum and Gonzalo Garcia put his side into a 3-0 lead.
Ulster responded almost immediately and drew level on 12 minutes, earning a penalty of their own right in front of the posts that Jackson was never going to miss.
Some desperate defending from Ulster prevented the hosts from getting the game's first try on 15 minutes but when they knocked on Garcia was able to come back for an earlier infringement and kick Zebre 6-3 ahead.
The Ulstermen came even closer to the try-line after some nice offloading from Cave, and Roger Wilson was felled just short as the recycled possession led to nothing.
Garcia then made no attempt to roll away from the tackle and was penalised when Zebre were under pressure once again - Jackson responding with the simplest of penalties on 23 minutes to again level things up.
The move of the match then allowed Ulster to score the game's first try with Jackson, Craig Gilroy and Cave all involved.
Jackson invited the challenge from the Zebre defence and produced a fantastic offload to Gilroy on his shoulder, who in turn was able to offload once more to the advancing Cave who then finished the move off under the posts - Jackson again with the conversion.
That's how it stayed until the end of the first-half but after the break Jackson picked up where he left off with two penalties to give Ulster a 19-6 advantage.
Zebre however did come storming back with a try of their own through Guglielmo Palazzani - the full-back going over in the corner with the Ulster defence stretching following multiple phases of play.
The hosts didn't help themselves moments later, however, as they were offside and again Jackson was presented with a straightforward penalty but this time the Irishman missed, the ball hitting the post.
With time running out Zebre's Mauro Bergamasco made a superb break to set up a try-scoring opportunity but frustratingly with a kick in behind the Italians were guilty of being offside and the chance went begging.
A high tackle from Dan Tuohy gave Zebre a chance to give themselves good field position in the Ulster half with four minutes remaining and after collecting the successful lineout they were on the attack.
But some fantastic defending from Ulster earned the Irish side the put in at the scrum and they held onto possession to see out the result which helps them keep pace with the sides above them.
Follow us on Facebook, join the conversation on Twitter, sign up to ourYouTube channel for extensive match highlights and sign up for our newsletter for regular updates on the RaboDirect PRO12

| Zebre Score Card | |||||
| Name | Tries | Conv | Pen | Drop | Pts |
|---|---|---|---|---|---|
| Gonzalo Garcia | 2 | 6 | |||
| Guglielmo Palazzani | 1 | 5 | |||
| Total | 1 | 2 | 11 | ||
| Ulster Rugby Score Card | |||||
| Name | Tries | Conv | Pen | Drop | Pts |
|---|---|---|---|---|---|
| Darren Cave | 1 | 5 | |||
| Paddy Jackson | 1 | 4 | 14 | ||
| Total | 1 | 1 | 4 | 19 | |
| |||||||||||||||||||||||||||||||
