But they could not find the fourth try which would earn them an extra point, ensuring they went four points clear of the Ospreys, who face the Blues later on Saturday at the Millennium Stadium.
Leading 16-13, Davies grabbed the crucial try for Scarlets on 66 minutes and North crossed for his second score two minutes later in a devastating short burst that accounted for the Dragons.
Scarlets began the brighter and earned the chance to break the deadlock on 11 minutes but fly-half Owen Williams saw his effort drift just wide.
He made no mistake on 19 minutes however as Scarlets continued to dominate the opening exchanges, knocking over his first penalty of the day after Wales No.8 Toby Faletau was called up for collapsing a maul and subsequently sent to the sin bin.
Dragons were struggling to get a foothold in the match and the Scarlets extended their lead on 26 minutes when Wales flyer North finished off a fine flowing move.
Owen Williams made the first break and found scrum-half Aled Davies inside, who immediately popped the ball back outside to the onrushing North who was not going to be denied after breaking the Dragons line.
Owen Williams converted and the Scarlets threatened to run riot when they were awarded another penalty, only for their fledgling fly-half to strike the post.
The Dragons then hit back and scrum-half Jonathan Evans darted through a gap after picking up from the base of a ruck, sold Scarlets prop Phil John a dummy and darted over against the run of play.
Tom Prydie converted and the Dragons continued to grow in confidence and pulled level despite the Scarlets' first-half dominance right on 40 minutes.
Scott Williams was penalised at the breakdown and Prydie booted his first penalty of the day as the sides went in 10-10 at the break.
The Scarlets, perhaps feeling they had the Dragons their for the taking in the first half, flew out of the blocks after the break and replacement hooker Ken Owens burst down the left but could not free his backs.
Owen Williams restored the Scarlets' lead from the tee on 45 minutes but that stirred the Dragons into life and the RaboDirect PRO12 strugglers began to exert their authority on the match.
It came from a superb break from fly-half Dan Evans, who found Will Harries on the right but he could not finish the job and the Scarlets came back to cover.
Harries made up for it soon after however with a superb break down the left but Davies darted down the blindside but was stopped just short by North.
The Dragons kept coming and finally had some points to show for their endeavour but it was three not five - Prydie drawing his side level again from the tee on 56 minutes.
But frustratingly for the Dragons, the Scarlets hit back almost immediately, Owen Williams on target from the tee before hitting the post soon after with another.
But then came the killer blow as Scarlets centre Scott Williams broke the Dragons line down the right and fed Davies on the right who was tackled but showed great improvisation to drag himself backwards over the try-line.
That took the wind out of the Dragons' sails and the Scarlets had their third try almost immediately.
Davies fielded the restart after Owen Williams had slotted the conversion and he, Gareth Owen and Owens combined to release North down the right and the winger streaked clear for his second score.
The Scarlets were in search of the fourth try that would secure the extra point but in doing so they left themselves open and the Dragons were the next on the scoresheet.
After concerted pressure saw the Dragons knocking on the door, the impressive Evans got the try his performance deserved, stepping over and dotting down for the score, converted by Prydie.
|Newport Gwent Dragons Score Card|
|Scarlets Score Card|