Under-strength Munster started their defence of the Magners League with a 22-9 defeat away to Glasgow.
Munster looked sharp in the opening minutes of the game but a penalty goal from Jeremy Manning was scant reward.
Then it was Glasgow's turn to show their attacking flair with a run out of defence by Bernard Stortoni that ended with Munster conceding a penalty at the break down and a score-levelling penalty goal from Parks.
It was the Glasgow outside half who engineered the next points with a towering kick that was skillfully taken by Ulster summer transfer Rob Dewey . In the ensuing scrap for the ball, Munster offended, allowing Parks to stroke over his second goal of the contest to give his side a 6-3 lead.
Cusiter inspired a rolling maul from his own sharp break round the fringes. Munster were penalised for illegally stopping it and Parks made no mistake with the head-on kick at goal.
Peter Stringer was sent to the sin-bin for not rolling away after the tackle and it was a straight target for Parks to put his side 12-3 in front at half time.
After the break Manning scored his second penalty and then Munster made two changes to their front row and Glasgow conceded a penalty at a set scrum giving Manning an easy shot at goal to reduce the lead to just three points.
Parks scored another penalty and then Ruaridh Jackson celebrated his first minute on the field with a glorious touch down, converted by substitute scrum half Mark McMillan to seal victory.