The home side had gone toe to toe with the Dragons for most of the game before letting the Welsh visitors move ahead late on to secure the points.
After an early Ceri Sweeney penalty Paul Dearlove put Glasgow ahead collecting the scoring pass from Andy Henderson who had barged through a sea of defenders. Parks converted from the widest of angles but the lead was short lived with Sweeney adding a second penalty before Jamie Ringer scored his side’s first try.
However Glasgow bounced straight back with Donnie Macfadyen touching down and Parks adding the conversion and a penalty to open a six point gap. But the lead see-sawed back to the visitors when poor defence allowed Kevin Morgan to wander over untouched for his side’s second try, Sweeney again adding the extras, while a third came when prop Rod Snow was driven over by the pack, and again Sweeney was on the mark with the kick.
Parks slotted a successful kick before the break and three more early in the second period, which saw Glasgow back in charge. However the Dragons were determined not to go home empty handed and a bonus point fourth try through Gareth Cooper edged them back into the lead, Sweeney securing maximum points with the conversion before adding another penalty.
Glasgow were then denied the consolation of a bonus point when Sione Tuipolotu slotted a late drop-goal.