Zebre could respond just once through a Daniel Halangahu penalty, leaving the Italians still without a win and bottom of the table.
Eager to atone from defeat in Belfast against Ospreys last time out, Ulster were quick out of the traps and at the first breakdown Luke Marshall put pressure on Paolo Buso's kick and charged it down, but the ball ran over the deadball line just before Darren Cave could reach it.
It appeared early pressure had paid off for the Northern Irishmen when in the eighth minute Andrew Trimble showed fine creativity with a one-handed pass around the tackle of Buso to find fellow wing Chris Cochrane in the left corner. Cochrane grounded the ball over the try-line but official Neil Paterson called for help from video referee Peter Ferguson who ruled Cochrane's trailing leg had gone into touch.
The hosts' disappointment was short-lived however, as from the resulting Zebre line-out Andrea Mancini's over-throw was quickly pounced on by hooker Herring who showed good strength to force his way over for the opening try under pressure from three visiting defenders, Pienaar landing the conversion.
This seemed to spark Zebre into life and they had the chance to get their first points on the board when Duncan Fitzpatrick gave away a penalty, but Halangahu's kick lacked power and fell short of the bar.
Ulster were playing with plenty of width as they attempted to bring Cochrane and Trimble into the game at every opportunity, but the intensity of Zebre's defending kept the league leaders at bay.
In the 34th minute Halangahu made no mistake with his second penalty opportunity of the game to reduce the score to 7-3.
Flanker Iain Henderson looked likely to score Ulster's second try shortly after before falling into touch, while Zebre wing Sinoti Sinoti showed promising signs for the visitors with a quick break.
Ulster finally got their second try just five minutes before the break, ensuring the ideal start and finish to the first half. Pienaar and Trimble combined effectively before Cave took over, the centre switching back inside to Diack for the number 8 to increase the lead to 12-3 at the interval, with Pienaar having missed the conversion.
With centre Gordon D'Arcy ruled out of the remainder of the Six Nations for Ireland, the performances of Cave and Marshall at 12 and 13 were of particular focus, and Cave was again involved as his side increased their lead to 17-3 in the 57th minute.
Trimble darted around the outside with a smart dummy before Pienaar cleverly recycled possession to find Cave who waited for Diack's run before releasing the South African to go over under the posts, Pienaar making no mistake with a simple conversion to earn a 19-3 lead.
This came after a try had been ruled out by the video referee when it was found that Henderson hadn't touched the posts with the ball when under pressure from Filippo Cristiano and Marco Bortolami, resulting in a five-metre scrum in the hosts' favour.
With seven minutes remaining Andrew's pace and power ensured a bonus point as he burst through to score his first of the season, Pienaar making it 26-3 from the boot.
|Ulster Rugby Score Card|
|Zebre Score Card|