The struggling Blues can rightly point to better set-pieces and an edge in territory and possession, but the Dragons defence were in top form and held them out for most of the game.
A lovely chip through by MacLeod saw Rhys Williams gather and dive over for a Blues try after eight minutes and MacLeod added a penalty to signal 20 minutes of total domination by the visitors.
After 25 minutes, however, Morgan was worked clear for his - and the Dragons’ - first try, and in the 34th minute a searing break by Montgomery carved open the Blues defence. Sione Tuipulotu completed the move with a try converted by Ceri Sweeney, giving the Dragons a 12-8 half-time lead.
In the second half, MacLeod and Sweeney exchanged two penalties apiece to make it 18-14. With two minutes left, Morgan took a midfield pass from Sweeney and sliced through for his second try, effectively winning the game for Dragons. Sweeney converted and although replacement Jonny Vaughton grabbed an injury-time try for the Blues - converted by MacLeod - Dragons held on to win.
In Scotland, injury-hit Edinburgh had a good win over Glasgow. Missing the likes of Chris Paterson, Scott Murray and Nathan Hines, Edinburgh can thank Hugo Southwell for a super performance. He surged over for their first try and set up Craig Joiner’s clincher late on with a clever kick.
Glasgow made a rip-roaring start, pinning the capital troops back inside their own danger zone, but they only earned three points from an Calvin Howarth penalty.
Edinburgh then battled back into the contest through their pack. Glasgow stepped up the pace again as the interval approached when Edinburgh were reduced to 13 men in the wake of yellow cards in quick succession for Ally Kellock and Lee.
Glasgow also showed more purpose in exchanges after the restart, stringing together a controlled sequence of ten phases. Howarth edged his side back in front with a penalty from virtually under the crossbar.
This gave Edinburgh a wake-up call, and within three minutes, Southwell had squeezed in at the corner flag for a try. The contest really hotted up as Howarth completed his penalty treble, but his next attempt crashed back off the upright.
Then Southwell sent a beautifully weighted kick towards the line which veteran Craig Joiner touched down. Substitute Phil Godman added the conversion and scored a try from a close-range penalty soon after. Dan Parks managed a late penalty to salvage a bonus point for Glasgow.