Debutant wing Kristian Phillips scored the Scarlets' only try as the west Wales region saw off Zebre to move up to second in the RaboDirect Pro12 table.
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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.