The match marked scrum-half John Cooney's 150th Ulster cap as the Dublin man led the team out in Belfast before KO.
Ulster were unlucky not to break the deadlock on 17 minutes after kicking a penalty to touch.
From the lineout, the forwards probed at the line with Scott Wilson, Lorcan McLoughlin and David McCann all being stopped close and after an eighth drive for the line the ball was knocked on allowing Zebre to clear their lines.
Ulster nearly opened up the Italian defence minutes later after Zac Ward launched a counter attack from his own 22. The winger showed all his sevens speed to go deep into the opposition half before passing to John Cooney, the scrum half however couldn't find Ward with the return pass and the visitors were able to clear the danger.
The deadlock was finally broken on 28 minutes after Zebre won a penalty from a scrum on the Ulster 22 right in front of the posts. Fly- half, Giovanni Montemauri, slotting the kick.
Zebre were reduced to 14 men on 32 minutes, as open side flanker Stavile was yellow carded for an off the ball tackle.
Ulster kicked the resulting penalty to touch and the forwards set up the driving maul. Hooker, Tom Stewart, peeled off the back and charged for the try line, but was bungled into touch by his opposition number, Luca Bigi.
Zebre nearly breached the Ulster defence in the final minute but good work at the break down from Stewart and Nick Timoney won an important turnover.
The half-time whistle went and Ulster were behind by three at the interval.
The Parma-based side got the match's first try seven minutes after the restart.
From a lineout, the forwards probed before scrum half, Gonzalo Garcia, made a sniping run before putting Bautista Stavile over in the corner for an unconverted try.
Zebre got their second try just two minutes later, from a quick tap penalty on the Ulster 22.
Italian full back, Giacomo Da Re, running a great support line to dart into space and finish for the second score. Montemauri converted for a 0-15 lead.
After a period of pressure, Ulster got back in the game on 56 minutes, with replacement prop, Corrie Barrett, barging over from close range.
Ulster's forward pack had probed at the line and Barrett went over after a series of pick and drives at the Zebre whitewash. Replacement scrum-half, Nathan Doak, added the conversion.
Zebre ten, Montemauri, then missed the opportunity to extend the visitor’s lead as he pushed a 65th minute penalty wide.
It wasn't to be the best night for kickers, as then Doak missed the chance to narrow the gap minutes later as his penalty went wide in the swirling wind.
The home side then set up a grandstand finish with a second Barrett try on 75 minutes.
Powerful surges from McCann and Timoney took Ulster close to the line, before the replacement tight head prop wriggled under a pile of bodies to ground the ball over the line.
Doak’s conversion narrowed Zebre’s lead to a solidarity point.
Ulster had one last chance to win the match as they kicked a penalty to touch.
The forwards set up a powerful drive with carries from Jude Postlewaite and McCann getting good territory, however the visitors won a penalty to end the match on what was a disappointing result for Richie Murphy's side.
Ulster will next be in action against Super Rugby side, Queensland Reds, who come to Kingspan Stadium in two weeks time.
Scorers
Ulster
Tries: Corrie Barrett x2
Cons: Nathan Doak x 2
Zebre Parma
Tries: Stavile, Giocana Da Re
Cons: Giovanni Montemauri
Pens: Giovanni Montemauri
Teams
Ulster:
(15-9) S Moore; M Lowry, B Carson, J Postlethwaite, Z Ward; J Murphy,J Cooney;
(1-8) E O’Sullivan, T Stewart, S Wilson, H Sheridan, K Treadwell, L McLoughlin, N Timoney (c), D McCann.
Replacements:
J Andrew, for Stewart 52 mins C Reid for O’Sullivan 49 mins, C Barrett for Wilson 46 mins, A O’Connor for Treadwell 49 mins, Matty Rea for McLoughlin 66 mins, N Doak for Cooney 49 mins, J Flannery for Murphy 59 mins, R Lyttle for Ward 69 mins
Zebre Parma:
(15-9) G Da Re; A Gesi, F Paea, D Mazza, S Gregory; G Montemauri, G Garcia;
(1-8) P Buonfiglio, L Bigi, M Hasa, M Canali, L Krunov, R Nasove, B Stavile Bravin, G Licata.
Replacements:
G Quattrini, L Franceschetto for Hasa 73 mins, J Pitinari for Buonfiglio 49 mins, G Ferrari for Nasove 57 mins, L Andreani for Canali 69 mins, T Dominguez, L Morisi for Mazza 76 mins, S Brisighella for Gregory 70 mins
Ref: B Breakspear.