The hosts started strongly in Parma with Ulster forced to absorb numerous waves of pressure in a tough first 10 minutes in which they conceded four penalties.
Zebre’s deserved first try arrived on 11 minutes as Matteo Canali broke off from a driving maul to dive over the line.
Ulster responded well and hit back with their first real attack on 20 minutes as Herring fed McAllister, who bundled over his first score for the province on his second start.
Momentum seemed to have swung further in Ulster’s favour when Gesi was shown a straight red card on 28 minutes, after a lengthy check by the television match official, for attempting to put his fingers in McCloskey’s eye.
Zebre did well to regroup from losing a man and they continued to look the side more likely to score next, but Giacomo Da Re squandered the chance to give them a half-time lead as he kicked a penalty well wide.
Ulster started better in the second half and went ahead on 43 minutes as Herring raced off the driving maul to cross in the corner.
They extended their advantage on 52 minutes as Zac Ward finished after substitute Juarno Augustus had made the decisive breakthrough and offloaded to the winger.
Murphy’s side pushed for the bonus-point against a tiring Zebre side and secured it when Kok touched down in the corner on 68 minutes.
Zebre kept fighting and scored a second try six minutes later as after a well-worked move, Jacopo Trulla chipped the ball forward and grounded in the corner.
Ulster’s attention will now turn to their European action next week when they face Welsh side Ospreys in the last 16 of the Challenge Cup.
Zebre: Da Re; Belloni, Bertaccini, Zanon, Gesi; Farias, Fusco; Hasa, Di Bartolomeo, Pieretto; Canali, Krumov; Ortombina, Stavile, Odiase.
Replacements: Quattrini, Pittinari, Neculai, Ferrai, Licata, Dominguez, Trulla, Morisi.
Ulster: McIlroy; Kok, Hume, McCloskey, Z Ward; Humphreys, McKee; O’Sullivan, Herring, McAllister; Henderson, Hopes; McCann, B Ward, Timoney.
Replacements: McCormick, Bell, Wilson, Dalton, Augustus, Doak, Carson, Moxham
