Paterson was their chief destroyer, capping a perfect kicking display - three penalties and three conversions - with a last-minute try to finish with a 20-point haul.
Scotland led 20-10 at half-time courtesy of tries from prop Bruce Douglas - his first for Scotland - and number eight Simon Taylor, with Paterson converting both and landing two penalties.
Wales' points came from a try by scrum-half Gareth Cooper three minutes from the break. Fly-half Stephen Jones, who had opened Wales' account with an early penalty, added the conversion to make it 17-10.
But Paterson responded with his second penalty, and the Scots had a 10-point cushion going into the second half.
Paterson's third penalty two minutes after the break put more pressure on Wales, who had to reorganise after having full-back Kevin Morgan carried off.
The visitors fought gamely, and Kenny Logan's pace saved Scotland when Gareth Williams kicked ahead into the corner looking for a try.
Scotland were then reduced to 14 men by the sin-binning of James McLaren, but though Wales had plenty of possession, the final pass went astray too often in the face of determined home defence.
Paterson hammered the final nail in Wales' coffin in injury time when Tom Smith's kick into the corner fell to Rhys Williams. He failed to ground the ball, and Paterson nipped in to claim the try.
Paterson added the conversion to make it 30-10, but Wales had the final say when they moved the ball swiftly out wide to create the space for centre Mark Taylor to go over for their second try.
Rhys Williams then made amends for his earlier blunder when he scampered through a sleeping Scottish defence for a third Wales try deep into stoppage time - but it was too little too late.