The 16-15 win saw last season's quarter-finalists make it to within one match of competing in the pool stages this time around, despite being second best for long periods against the plucky Quins.
"The way we played without the ball was the difference, our defence was excellent," said Llanelli head of rugby Anthony Buchanan.
"It was always going to be a close game. Credit to Quins, they came down and looked to attack us.
"There is a lot to work on, but it's the start of the season. We will look forward to Llandovery on Saturday now."
Llanelli had led 16-9 at half-time though the Quins will have felt hard done by having had the better of the first half.
The opening 40 minutes had predominantly been a kicking contest, fly-halves Josh Lewis and Craig Evans kicking three penalties apiece to make the score 9-9 with precious first half seconds remaining.
But in what proved to be the crucial moment of the match, Llanelli launched a sparkling attack from deep through full-back Dion Jones, a break that led to Josh Adams cutting inside to score.
The Quins reduced the arrears with a fourth Evans penalty shortly after the restart before Llanelli were denied a second try when referee Nigel Owens ruled out a Kyle Evans score.
Owens then yellow carded Llanelli flanker Dan Thomas for an infringement at a ruck and although Quins pressed late on, a penalty from replacement full-back Aled Thomas was all they could manage in reply.