The injury-hit Wales lock had been restricted to just three appearances for his new club after sitting out the World Cup with a back injury.
But Owen looked back to his best with a try in each half as the Dragons marched to their fourth successive win thanks to a convincing 38-15 over the struggling Scots.
Percy Montgomery, who also booted 18 points, and Sione Tuipulotu ensured a bonus point for the Dragons.
Meanwhile Leinster edged a thriller against leaders Ulster 32-30 at Donnybrook while Ronan O’Gara scored the only points as Munster won 3-0 at Connacht.
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