Centre Josh Matavesi scored a try five minutes from time to keep alive Ospreys' European Champions Cup quarter-final hopes at the Liberty Stadium.
French challengers Racing Metro moved level on points with English champions Northampton at the top of Pool Five, but they left Swansea disappointed after leading throughout the contest until Matavesi struck and Dan Biggar converted.
Racing responded to Saints' Pool Five bonus point win against Treviso earlier on Saturday by racing into a 13-point lead, before being hauled back and having to settle for a 19-19 draw.
Lock Francois van der Merwe's 18th-minute try, plus 14 points from the boot of fly-half Johan Goosen, looked to have preserved Racing's 100 per cent pool record, but Matavesi had other ideas.
Biggar also kicked four penalties for the Ospreys, but two points gained might still not be enough following an encounter when Racing's dominant forwards deserved more for their efforts.
Although there are likely to be a number of twists and turns before the quarter-final line-up takes shape next month, Racing's trip to Northampton in late January already looks like being a group decider.
But the Ospreys have at least given themselves a fighting chance, spurred into a second-half revival largely through the combined excellence of Wales internationals Rhys Webb and Justin Tipuric.
Biggar was among four players in the Ospreys line-up who started last weekend's Wales win against South Africa, being joined by his half-back partner Webb, hooker Scott Baldwin and lock Alun-Wyn Jones.
Racing, meanwhile, included Wales' current reserve scrum-half Mike Phillips against one of his former teams, but centre Jamie Roberts, who enjoyed an outstanding run of Test match form throughout November, was rested ahead of next weekend's Ospreys return fixture in Paris.
Goosen, deputising in the Racing number 10 shirt for Ireland star Jonathan Sexton, kicked a fourth-minute penalty that rewarded initial forward dominance, before he doubled his team's advantage shortly afterwards.
The Ospreys were slow to find continuity, but Webb sparked a 13th-minute attack that ended with Racing infringing inside their own 22, and Biggar's angled penalty halved the deficit.
There was no escaping, though, Ospreys' significant sense of strife up-front as Racing used an impressive driving maul to make considerable headway, and there could be few complaints when Van der Merwe scored out wide before Goosen landed the touchline conversion.
Ten points adrift inside the opening quarter, Ospreys required a considerable injection of pace and power in their game, yet despite Webb's best promptings, they continued to come off second-best to a rampant Racing pack.
And Racing's dominance was again underlined when the Ospreys resorted to illegal means to halt another maul, and English referee J P Doyle had no hesitation in sin-binning Wales international back-row forward James King.
Goosen rubbed salt into the wound by completing his penalty hat-trick, and although Biggar quickly replied for the home side, there was no doubting Racing's supremacy in all critical areas.
The Ospreys, who were without their leading loosehead props Nicky Smith and Duncan Jones because of injury, somehow had to start moving Racing away from the set-piece game they were so keen on playing, but they could have complaints about a 16-6 interval deficit.
There were more encouraging signs early in the second period as Ospreys pressed, yet Biggar missed an easy penalty chance before Webb's break and kick ahead just failed to find chasing wing Eli Walker, who was beaten to the ball by his opposite number Adrien Plante.
Biggar made amends for his uncharacteristic blunder by cutting the gap with his third successful penalty four minutes later, and there was a far greater sense of urgency about the home team as they tried to heighten their attacking tempo.
A fourth Biggar penalty gave Racing further food for thought, but just when it looked as though Goosen's 73rd-minute drop-goal would be enough, back came the Ospreys with Matavesi's superbly-worked touchdown that Biggar converted to secure a share of the points.