Tom Prydie booted the hosts into the lead but from there it was one-way traffic.
The Scottish side ran in eight tries to leave the Dragons staring at a humiliating loss – their worst ever in all competitions
Prydie fired the Dragons into the lead after just one minute at Rodney Parade but Scotland international Duncan Weir quickly hit-back.
The visitors, who boasted a far more experienced side than the Dragons, soo took control of the encounter.
Ryan Wilson and Mark Bennett combined on the counter-attack and following a sustained period of pressure the centre dummied his way over.
Weir converted and Glasgow swiftly stretched their advantage with Matawalu collecting Henry Pyrgos’ chip.
Matters only got worse for the Dragons as Glasgow continued to dominate affairs and Weir kept the scoreboard ticking.
And they took a giant stride towards victory with Alex Dunbar cruising over after receiving the ball from Weir on the switch.
Weir converted the effort to hand the visitors a 27-3 lead at the break.
The Dragons were much improved following the break but it was not enough to find a way back into the encounter.
Glasgow wrapped up the bonus-point thanks to Paris. The wing had barely been on for a minute when Dunbar bulldozed through the Dragons midfield and he was on hand to collect the centre’s offload.
That saw the floodgates open and Glasgow added a further four tries with Swinson, Strauss and Thomson all crossing.
