Taylor averaged 75.77 as he battled to an 8-4 victory over Hedman. Both players shared the first six legs before The Power began to build a lead.
The 61-year-old rallied off the next three legs, including a 14-darter, as he moved 6-3 ahead.
Hedman closed the gap by taking out the next leg in 15 darts, but that only delayed the inevitable as Taylor won the next two legs to secure his place in the quarter-finals.
Earlier in the night, Hedman had to come through her preliminary round match against Trina Gulliver.
The 62-year-old averaged 71.51 as she battled past her long-time rival, winning the match 8-5.
Northern Ireland's Colin McGarry won the other preliminary round clash as he powered past Keith Deller.
McGarry posted the highest average of the night, as his 89.73 helped him to a comfortable 8-3 victory.
The 56-year-old won the first three legs to take a commanding lead, but Deller fought back in style and won the next two.
McGarry was then able to find another gear as he won five of the next six legs, including three 14-darters, to seal a first-round clash against Peter Evison.
Elsewhere, Kevin Painter booked his spot in the quarter-final with a whitewash 8-0 victory over John Lowe.
The 2004 PDC world championship runner-up kicked off the match with a 15-darter and finished things off with a 12-dart leg.