The excellent Robbie Diack scored a brace of tries as Ulster retained their seven-point lead at the top of the Pro12 despite producing yet another frustrating performance.
Following much huffing and puffing at Ravenhill, it was not until the 73rd minute that Ulster accrued their bonus point after full-back Ricky Andrew dived over. It was his first try for Ulster, with hooker Rob Herring also getting off the mark for the province with an early effort.
However, against the bottom team in the league who have yet to register a point, Ulster toiled. On a dour night, Chris Henry followed Luke Marshall to the treatment table, both men suffering leg injuries.
At least Iain Henderson shone for the hosts and he snuck the man-of-the-match award from Andrew Trimble and Darren Cave.
Unlike recent games, Ulster started with some urgency. First Cave almost got the touchdown after a blocked kick and then a wonderful Ruan Pienaar break just failed to bag the opening try.
However, after serious pressure in the red zone and a disallowed try by winger Chris Cochrane, Ulster stole a Zebre line-out which enabled hooker Herring to score his first try for the province with eight minutes on the clock. Pienaar added the extras. Ulster's momentum was halted however by handling errors that were reminiscent of the Aviva Stadium last Sunday.
Indeed, Ulster appeared to fall into some kind of slumber for 20 minutes as they absorbed Zebre pressure and their apparent lethargy was punished when Daniel Halangahu banged over a straight-forward penalty in the 33rd minute.
That seemed to stir Ulster into life again, but despite a flurry of activity the scoreboard stayed the same. The home fans found their voice after great work by Pienaar and the busy Trimble down the right suddenly saw the action swing upfield, with Diack scoring wide on the left after a sweet inside pass from the industrious Cave. Immediately on the restart, Cave was again to the fore as Ulster searched for their third try, with Henderson grounded short of the upright as he broke through two tackles.
But Zebre's resistance finally crumbled when first Trimble scythed through only to be stopped just short of the line before the ball was recycled again and Cave made the half-break to feed Diack for his second try, which was again converted by Pienaar.
It was all hands to the pump for Ulster as news filtered through that second-placed Glasgow had already chalked up a clatter of tries in Newport.
Error after error thwarted Ulster efforts to clock up more points, but after the replacement bench was emptied, their was fresh impetus and the decibels rose among the support when full-back Andrew skipped through a gap on the right to score the bonus-point try.
Ulster – R Andrew; A Trimble, D Cave, L Marshall (Olding, 37), C Cochrane (Walsh, 56); P Jackson (Heaney, 68), R Pienaar; T Court (Black, 68), R Herring (Annett, 65), D Fitzpatrick (Afoa, 40), J Muller, capt, L Stevenson (McComb, 68), I Henderson, C Henry (McComish, 50), R Diack.
Zebre – P Buso; L Sarto, A Benettin (Chiesa, 71), G Garcia, S Sinoti (Odiete, 46); D Halangahu (Pratichetti, 38), A Chillon; A de Marchi (Aguero, 47), A Manici (Festuccia, 48), L Redolfini (Fazzari, 48), M van Vuren, M Bortolami, capt (Belardo, 54), F Cristiano (van Schwalkwyk, 46), M Bergamasco, J Sole.
Ref – N Paterson (SRU).