The sides went into the match on the back of contrasting recent fortunes. Glasgow were smarting from the last-gasp narrow defeats at the hands of French giants Biarritz in France and local rivals Edinburgh in the festive showdown at Murrayfield.
The Dragons, on the other hand, travelled north in buoyant mood in the wake of their surprise triumph over the Llanelli Scarlets last time out.
It was the home side who drew early encouragement when Rugby World Cup stand-off Dan Parks confidently slotted a penalty in the third minute for offside at a midfield ruck. The Dragons continued to look jittery, having had only a handful of days respite following the Scarlets encounter. And they fell further behind in the sixth minute when Parks was again on target.
His second strike acted as a wake-up call for the Gwent brigade and they powered their way back into the contest with a fine try by flanker Joe Bearman after a concerted spell of pressure in the danger zone.
Ceri Sweeney followed up with an accurate conversion to enable the Dragons to sneak in front midway through the half. Sweeney jumped back into the spotlight on the half-hour mark to clip over a penalty to stretch the Dragons' lead.
Both teams carved out chances in the approach to the interval, but the respective marking proved more than adequate. Glasgow's efforts to get back on terms in the opening stages of the second half proved fruitless.
Their plight deepened in the 51st minute when Sweeney thumped over his second penalty to widen the gap to seven points.
The Warriors awoke from their slumber to level the tussle midway through the half. Scrum half Sam Pinder was in the right place at the right time to reach the line in typically sniping fashion following slick inter-passing among the home ranks. Parks added the extra points to set up a fascinating final quarter.
Glasgow should have seized the initiative but it was the Welsh region who upped the ante to grab the lead at a crucial stage; Peter Sidoli was the man who mattered as he bludgeoned his way to the line from close quarters.
Sweeney was off the mark with the conversion bid and the excitement level rocketed as Parks completed his penalty treble, reducing the leeway to two points in the process.
The home fans then held their heads in despair when they watched Parks's last-gasp drop-goal attempt slide wide of the post by a matter of inches. Then Johnnie Beattie was blocked just a pace short of the line as time ran out.