The stand-off was snubbed for the autumn Test series but he produced a stunning performance to take the Warriors to the top of the Magners League on points difference from Edinburgh.
Parks claimed a tally of 20 points with his accurate boot, and also helped to set up Glasgow’s try by Thom Evans.
Warriors had struggled to find a rhythm in a scrappy first half and turned round seven points in arrears.
But with the fierce gale and driving rain at their backs, they had high hopes of stealing the initiative after the restart. And Parks obliged in style.
The stand-off had edged them in front after just three minutes with a close-range penalty, only for Ian Humphreys to strike twice in quick succession to take his side into the lead.
There were further alarm bells for the Warriors five minutes before the break when prop Tom Court was driven over.
Humphreys added the extras, however there was still time for Parks to claw back three points with the last act of the half.
Parks jumped back into the limelight immediately after the interval by banging over a 50-metre penalty.
The confidence of the stand-off was sky-high and there were gasps of disbelief when he opted for another pot at goal from well inside his own half.
But his self-belief proved entirely justified as the ball sailed between the uprights, slashing the leeway to a single point.
The amazing run of success for Parks continued five minutes later when he hit the target yet again.
Ulster came back into the reckoning with a sequence of forward-orientated moves, but they were up against a resolute visiting defence.
Both sides made wholesale substitutions as they geared up for the decisive last quarter.
It was Glasgow who got the scoreboard rattling again – Parks firing over penalty No.6 to establish a five-point cushion.
Then came the moment that ensured the Warriors’ success.
A steepler by Parks created panic among the Ulster back-ranks and Chris Cusiter sniped down the narrow side to send winger Thom Evans sliding over in the corner.
And despite the width of the angle, Parks clipped over the conversion to seal the win.
Ulster C Schifcofske; T Nagusa, D Cave, I Whitten, S Danielli; I Humphreys, I Boss; T Court, A Kyriacou, D Fitzpatrick, D Tuohy, R Caldwell, D Pollock, W Faloon, C Henry (capt).
Subs: N Brady, B Young, E O’Donoghue, T Anderson, P Marshall, N O’Connor, J Shiels
Glasgow Warriors B Stortoni; A Dunbar, M Evans, G Morrison, T Evans; D Parks, M McMillan; J Welsh, D Hall, M Low, T Barker, R Gray, K Brown, J Barclay (capt), R Vernon.
Subs: F Thomson, K Tkachuk, D Turner, C Forrester, C Cusiter, C Gregor, P Murchie.
Referee J Jones (WRU)
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