Pienaar struggled with the boot kicking just ten points but Craig Gilroy's try 12 minutes after the break eased the pressure despite second-half yellow cards to Willie Faloon and Ian Whitten.
Newport could only record four penalties from Jason Tovey as their winless away run continues with centre Stefan Terblanche ensuring Ulster earned a bonus point with a fifth try at the death.
It didn't take long for the game to burst into life as a Gavin Thomas pass was superbly intercepted by Ian Humphreys with the Ulster fly-half charging into Dragons territory.
Under pressure from Tovey, Humphreys sent a kick tumbling out but he moved quickly to restart play after an apparent touch from the Dragons No.10.
He feed Pienaar who set up back row Mike McComish to score however it wasn't to stand as referee Carlo Damasco pulled proceedings back for a Newport line out.
The visitors made the most of the decision to take the lead four minutes later, Tovey slotting a fine penalty, with Pienaar missing the opportunity to level the score moments later.
However it hardly seemed to matter as in the 13th minute a clever quick lineout saw No.8 Diack collect and power over for the first try of the game.
Pienaar sent the conversion wide but was on hand to finish Ulster's second try moments later as Newport allowed the hosts to sweep through their defence.
With the conversion right in front of the posts Pienaar comfortably slotted his first points with the boot with Ulster threatening to run away with the tie at 12-3.
Newport hit back with two Tovey penalties in the space of five minutes however Pienaar responded with a well-taken kick and three points of his own for Ulster.
And, while the first half was lit up early on, it took ten minutes for the first points of the second half to be scored courtesy of Tovey's fourth penalty of the night.
However Ulster extended their lead straight from the kick-off, Nevin Spence making a nuisance of himself as the ball dropped, and Humphreys eventually feeding wing Gilroy to score.
Pienaar missed the conversion as Ulster moved into a 20-12 lead but they were reduced to 14 after Faloon was given a yellow card for not releasing in the tackle following a number of warnings.
Newport pressured but couldn't find a way through, even when Whitten received a yellow card for hands in the ruck, with a Pienaar penalty and Terblanche's converted try completing the scoring.
|Ulster Rugby Score Card|
|Newport Gwent Dragons Score Card|