Coach David Rees saluted Newport's third win in a week as a "magnificent effort".
Rees, also backs coach with Wales U-21s, had flown home early in the morning after their Athlone win over Ireland.
"Newport have had three tough fixtures in a week - beating Aberavon in the cup, Llanelli in the league and now this double over Llandovery," said Rees.
The Black and Ambers also bid for a double in each of their next two matches - at Bridgend on Saturday and at Maesteg on March 8 in a preview of their Konica Minolta Cup quarter-final.
Outside-half Daniel Griffiths clinched the latest win with 14 points - four penalties in five attempts and converson of lock Neil Watkins' 14th-minute try after a lineout.
"I think we were the better side," said Rees, and victory came despite Newport having players with the Wales age groups and Crawshays team in Ireland.
Griffiths kicked 16 points in the 26-25 win at Llandovery in September, when the Drovers missed a penalty with the last kick of the match.
Newport lead the West Walians 6-0 on the head-to-head league count over the past three seasons.
The programme said that in the five previous matches Newport scored 32 tries and Llandovery 13, a total of 45 tries at nine a game.
This latest fixture was different, however, with the strong, cold wind making long passes, lineout throwing and tactical kicking hazardous.
Scoring ended with Griffiths' last successful penalty after 52 minutes.
But frozen spectators had to endure 11 minutes' stoppage time by Ystrad Mynach referee David Davies.
The Black and Ambers, 13-6 up at the interval, were stretched in the last quarter when Llandovery were three times denied tries with their forwards camped on the home line.
No 8 Sam Waldron set a great standard in defence and attack for Newport.
In those lineouts where throwing beat the conditions, Watkins and fellow lock Matthew Veater were formidable. Full back Ricky Williams was sound under the high ball.
Llandovery scrum-half Rob Walters was yellow- carded midway through the second half.
Another technical infringement later sin-binned flanker Richard Dale, 14 minutes after coming off Newport's bench.
Dragon David Maddocks and Adam Brown, of the Dragons Academy, both went into the pack as second-half replacements.
Newport: R Williams, G Chapman, R Shorney (capt), R Payne (J Rowles 69), R Fussell, D Griffiths, A Walker, D Pattison (D Maddocks 52), L Jones (R James 68), G Robinson, M Veater, N Watkins (A Brown 68), C Davies (R Dale 60), S Waldron, P Williams. Scorers: Try - N Watkins; cons - D Griffiths; pens - Griffiths (4).
Llandovery: I Davies, M Bowen, H Thomas, J van Wyk, D Evans, T Marks, R Walters, D Williams, A Yelland, A Jones, T Walker, A Davies (capt), C Davies, J Mills, G Thomas. Scorers: Pens - T Marks (3). Referee: D Davies (Ystrad Mynach).
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules hereComments are closed on this article