That chance came after Hook's superb tackle on Thomson, knocking the ball out of the hooker's hands with the force of his challenge before tapping it back one-handed to Williams to strut his stuff.
Biggar converted, but after the restart the Ospreys fluffed another chance as centre Andrew Bishop's over-elaborate pass killed the move and led to the penalty that allowed Parks his first, unsuccessful, shot at goal.
Irish referee George Clancy warned Marty Holah and Rob Dewey after they clashed off the ball and prop Edward Kalman earned the ire of home fans for a clumsy high tackle on Williams.
In the meantime the Ospreys went close when Ali Kellock's line-out tap-back allowed hooker Huw Bennett and scrum-half Mike Phillips to create some nervous moments for the visitors' defence.
Rob Dewey and Marty Holah face off as tempers fray in the big game
However, Glasgow proved equal to the Ospreys' scrum power to clear their lines and the danger.
Glasgow's resilient defence had been the platform on which their top-four finish was built and - Williams' early try notwithstanding - they were able to frustrate the home side's attacking ploys.
But Parks failed with his second penalty attempt after 34 minutes and Glasgow's most promising attack was halted as centres Max Evans and Graeme Morrison were caught crossing.
Mike Phillips returned the favour when he took on too much responsibility and found himself smothered in defenders.
The action was growing increasingly frenetic and demanded a calming influence that might have profited either side.
Ospreys fans saw their side spill the ball on numerous occasions with full-back Lee Byrne and skipper Ryan Jones among the guilty parties.
That helped ensure the Ospreys led only by Williams' try and Biggar's conversion at the break.
With the second-half barely underway Bishop's sliced clearance gave Glasgow an attacking platform they craved and they made the most of the chance, albeit in surreal circumstances.
A dejected Warriors squad reflect on defeat and the end of their season
Thomson overthrew at the line-out, only for Holah to tap the ball back into no-man's land for scrum-half Mark McMillan to gather and send the Glasgow hooker charging over at the corner with home skipper Jones unable to halt his progress.
Parks failed with the angled conversion, his third miss at goal in three attempts.
At the other end a Hook break came to nothing when his forced pass to skipper Jones brought another knock-on.
Apart from the Ospreys' self-inflicted pressures, Parks' tactical kicking was mostly superior to that of Biggar.
But after the home side stole a line-out from Glasgow, Phillips was able to launch the move that gave the home fly-half the chance to kick a 45-metre penalty.
Biggar blew another Ospreys try-scoring chance as he knocked on, but after clearing upfield Glasgow were then left to ponder the vagaries of officials' interpretations of the advantage law.
Williams gathered, set up a ruck and Hook stole away on the blind-side before chipping ahead and racing on to score, Biggar converting.
The try was given, I know I was pretty close to the line but I'll take the five points
Moments later Jerry Collins took a heavy blow to the head and Ian Gough came on believing he was a blood replacement.
But as the All Black staggered towards the touchline and was then helped on his way, it was clear he would not return.
Collins' fellow Kiwi Filo Tiatia had already entered the fray to possibly his last home appearance before retiring.
Glasgow's ex-Welsh rugby league international and Scottish Sevens player Hefin O'Hare made an impact with his creative instincts after replacing Dewey and the visitors' back-row of John Barclay, Kelly Brown and Johnnie Beattie lived up to their impressive reputations.
However, Glasgow were unable to build on Thomson's try and Biggar's late penalty put the contest beyond doubt.
Having predicted the Ospreys' front five may prove too powerful for the visitors, head coach Sean Holley was proved right even if they were again suspect at the line-out.
Glasgow went to Swansea with the best wishes of a nation ringing in their ears and they will return to the sound of justified plaudits for their efforts even if their search for silverware is now over.
Ospreys wing Shane Williams: "The try was given, I know I was pretty close to the line but I'll take the five points.
"It's always tough against Glasgow, they didn't come here to lie down and they've been tremendous away from home all season.
"We made far too many mistakes in critical areas, but a win's a win."
Ospreys coach Sean Holley: "It feels great, I thought we deserved it - fair play to the boys, they dug in and got the win.
"It's just great to be in the final, but we'll be wearing red shirts [to support Munster against Leinster] on Saturday."
Glasgow head coach Sean Lineen: "We didn't get the rub of the green anywhere, which was very frustrating.
"Perhaps we did not play enough territory and we played a bit too much in the final third when we just needed to put it in the corners.
"The Ospreys' two tries came from turnovers and that's how they get their momentum.
"The number of players they take off the ball - they should be playing American Football. It's unbelievable but they get away with it, so good on them."
Ospreys: Byrne, Bowe, Bishop, Hook, Williams, Biggar, M. Phillips, James, Bennett, A. Jones, A. Jones, J. Thomas, Collins, Holah, R. Jones. Replacements: Walker for Bishop (58), Owen for Hook (80), Nutbrown for M. Phillips (78), Shervington for Bennett (78), Bevington for A. Jones (71), Gough for Collins (62), Tiatia for R. Jones (58).
Glasgow: Stortoni, Dewey, M. Evans, Morrison, van der Merwe, Parks, McMillan, Kalman, Thomson, Low, Barker, Kellock, Brown, Barclay, Beattie. Replacements: Shaw for Stortoni (41), O'Hare for van der Merwe (58), Weir for McMillan (80), Tkachuk for Kalman (35), MacArthur for Thomson (71), Eddie for Barker (67), Turner for Kellock (58).
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