But the Scarlets, indebted to 17 points from the boot of outside-half Aled Thomas, made hard work of the victory against the Italian outfit, who have now lost all seven of their matches this season.
The Scarlets were without all 12 of their Wales squad players, giving former Ospreys duo Phillips and Gareth Owen a chance to start.
Zebre made a late change with full-back Ruggero Trevisan pulled out just before the start to be replaced by Alberto Benettin.
It was the Italians who took the lead on 13 minutes with a penalty for Daniel Halangahu after prop Deacon Manu had transgressed at a ruck.
But Halangahu missed two chances to double the lead on 18 and 22 minutes as the Scarlets struggled to get any pattern into their game and spent a lot of the first period trying to get out of their own half.
Both Owen and Italy flanker Filippo Ferrarini were yellow-carded by referee Dudley Phillips for an off-the-ball scrap.
The Scarlets then levelled the scores on 36 minutes when Thomas put over a penalty after a collapsed scrum.
But Zebre were back in the lead two minutes later when Halangahu kicked his second penalty, and in the dying seconds of the half Thomas' second penalty attempt rebounded off the left upright.
At the start of the second half the Scarlets gained more of a foothold in Zebre territory as the Italians had scrum-half Tito Tebaldi sent to the sin bin for pushing a n opponent.
The Scarlets got back on level terms for a second time with a penalty for Thomas on 48 minutes from a scrum offence by Zebre.
And the home side went ahead on 55 minutes with a long-range Thomas penalty as the Scarlets gradually got the upper hand up front and behind.
However, Zebre launched a counter attack after the Scarlets lost ball in the Italian 22 with centre Matteo Pratichetti diving over for a converted try and Halangahu adding the extra points.
The Scarlets refused to panic, though, and cut the deficit with a fourth penalty for Thomas before Phillips sped into the right corner after Zebre failed to gather a box kick from replacement scrum-half Aled Davies.
Thomas converted the try and then put over his fifth penalty two minutes from time to take Zebre out of losing bonus point range.
Danie Poolman crowned his home debut with a try as Connacht battled past Treviso 18-3 in a drab RaboDirect PRO12 affair at the Sportsground.
Former Stormers player Poolman, making his first start for the Irish province at outside centre, touched down to help the hosts to a 13-0 lead at the break.
Treviso's only reply was a crisply-struck penalty from Alberto Di Bernardo, but neither side managed to impress in attack amid scenes of heavy rain and strong wind.
Connacht closed out their third win of the league campaign, moving up to eighth place in the process, with a late try from fit-again captain Gavin Duffy.
Tiernan O'Halloran, fresh from training with the Ireland squad, made an early incision and Dan Parks pinged the opening penalty through the posts in the seventh minute.
With the wintry conditions leading to multiple mistakes, Connacht were unable to make much headway although Parks provided some welcome direction from out-half.
The former Scotland international added a second penalty before showing great awareness to dink through a kick which led to the westerners' first try.
Young full-back Robbie Henshaw led the chase onto Parks' well-weighted punt, toe-poking it on and the onrushing Poolman did well to score after some assistance from O'Halloran. Parks converted unfussily.
The understrength Italians, despite Brendan Williams' best efforts, were unable to threaten in the home 22 in reply and a malfunctioning lineout was their biggest cause for concern.
Treviso did improve in the second period and seemingly lifted their game after replacement Giulio Toniolatti saw yellow on the hour mark.
Out-half Di Bernardo raised their hopes of a late push for a losing bonus point as he slotted a 61st minute penalty.
He struck the post with a second penalty attempt, eight minutes from time, before Connacht produced a strong finish to settle the issue.
Parks watched a penalty kick fade away to the right, but replacement John Muldoon's determined run from the restart took him past two defenders and the ball was worked wide for Duffy to dive in at the corner.
The Mayo man touched down just moments after being brought on as a replacement, completing his comeback from a recent hamstring injury. Parks missed the conversion but Connacht were out of sight.
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