Patchell had landed two penalties and a conversion of a penalty try before, having missed a conversion of wing Tom James’ late try, he booted a touchline three-pointer to seal a 21-20 victory.
The Dragons had been 17-6 up during the second half after wing Ashton Hewitt scored a first-half try and fly-half Dorian Jones kicked three penalties and a drop goal, with Jones’ replacement Jason Tovey kicking a fourth penalty.
The win sends the Blues above the Dragons into ninth place in the Guinness Pro12 table.
At Murrayfield, Edinburgh sent Glasgow packing 23-11, in a game that doubled as the first leg of the inter-city 1872 Cup. The hosts fell behind to Mark Bennett’s early try but hit back to win with scores from Matt Scott and John Hardie.
Alan Solomons’ team now leap-frog Glasgow into the top six ahead of next Saturday’s Scotstoun return.
Warriors took just seven minutes to unpick the meanest defence in the Pro12 as they started brightly.
Leone Nakarawa and Fraser Brown combined to win turnover ball on halfway before the big Fijian lock drove the visitors into scoring range.
With a patient look, Gregor Townsend’s team played through a couple of phases before Finn Russell slotted in Bennett to crash over for the opening try. Russell, though, missed his conversion.
Warriors failed to build on that positive start and were themselves cut open six minutes later. It was brute force which saw Cornell du Preez run over the top of Russell as the number eight broke down the right, popping off at the perfect moment to allow Scott to run in for a score in the corner.
Edinburgh scrum-half Sam Hidalgo-Clyne added the extras along with a penalty before half-time as Glasgow, who also saw Bennett miss a long-range kick, went in 10-5 down. Russell and Hidalgo-Clyne traded a couple of kicks each as the opening 20 minutes of the second half saw the teams go blow for blow.
But the longer the match wore on, the more Edinburgh’s might in the forward areas told and they finally capitalised with 10 minutes left. Ben Toolis palmed a line-out down for Hardie who virtually staggered over the whitewash as the Glasgow defence disintegrated. Hidalgo-Clyne again converted.
The visitors piled forward in the closing stages looking for a score which would offer a losing bonus-point but the Edinburgh defence, which has conceded fewer tries than any other Pro12 side this season, stood firm for a morale-boosting win.
In Italy, Andries van Schalkwyk grabbed a last-gasp try to lead Zebre to a thrilling 28-25 victory over Treviso at the Stadio Sergio Lanfranchi, Parma.