Ospreys welcomed back Welsh stars Alun-Wyn Jones and James King who formed a strong second row, as part of a starting line-up which still only boasted four internationals.
But an outstanding kick from Parks put their line-out under early pressure, the fly-half finding touch six metres from the Ospreys line inside the opening ten minutes.
And after the resulting throw wasn't straight, Brett Wilkinson earned his side a penalty in the scrum and Parks made no mistake from the tee, sending the ball between the posts for an early 3-0 lead.
In response, Ospreys produced a powerful scrum of their own and in winning a penalty Matthew Morgan found the corner five metres from the Connacht line.
The Welsh region claimed the line-out with ease and forced another penalty, from which a quick tap and go from scrum-half Fotuali'i resulted in the game's first try on 11 minutes as the Samoan dived for the line.
Morgan added the conversion for a 7-3 lead but five minutes later the hosts were in front once more as Faloon touched down after a sweeping move.
A good offload from John Muldoon was followed by good play from Michael Swift, with the ball eventually finding Faloon's hard line. Parks kicking the extras from a tough angle to take the score onto 10-7.
The confident fly-half then attempted a penalty on halfway in the 19th minute and although his effort had the distance against the wind, his effort sailed just wide.
More impressive scrummaging from the Connacht front five driving the visitors back, resulted in another opportunity for Parks who extended the lead to 13-7 from 30 metres with his third kick from four.
More poor discipline from Ospreys early in the second half allowed the Irish side the opportunity to gain the upper hand and Parks slotted the ball over for a two-score lead at 16-7.
Great vision from the former-Scottish international put the Ospreys backs under immense pressure and although a speculative drop-goal from the fly-half on 53 minutes went wide, Connacht were the dominant force.
There was still fight in the visitors, who were looking to remain in a play-off position, as 20-year-old Morgan kicked a penalty to cut the lead to just six points with ten minutes remaining.
But minutes later an outstanding chase from Robbie Henshaw, Eoin Griffin and Danie Poolman, after Parks hung up a great kick, put Richard Fussell under serious pressure and forced him to concede a penalty.
Parks was successful once again but he wasn't finished there as three minutes later he added a drop-goal to take his tally to 17 points and seal the victory by 22-10.
There was still time for King to be sin-binned in the last action before the final whistle for a spear tackle, summing up a disappointing evening for the Ospreys.
|Connacht Rugby Score Card|
|Ospreys Score Card|