The Welshman picked up the final victory after impressing throughout the evening after blasting his way through world number two Luke Littler 6-4 and world number one Luke Humphries 6-3 earlier on.
The win is the first for Price this season in the Premier League.
Price averaged 100.57 against Aspinall and narrowly missed out on a nine-darter in his opening match of the night.
Night Two winner Littler looked notably frustrated after his first-round defeat in Ireland, throwing his equipment to the ground in anger on his exit from the stage.
The Iceman was particularly impressive on the doubles all night, pinning tops to seal the win after finding 50 per cent of his checkouts (6/12) compared to The Asp's 37.5 per cent (3/8).
Aspinall - who had been struggling with illness this week - defeated Rob Cross and Michael van Gerwen en route to the final.
The results mean Luke Humphries remains top of the table with 10 points, while Price moves into second and Littler down to third.
The Premier League season continues next Thursday from Exeter.