Woodhouse will face Stephen Bunting in the next round after the eighth seed saw off Latvia’s Madars Razma in the last game of the afternoon session.
Bunting, the reigning Masters champion and former BDO world champion, put in an accomplished display to secure a 4-1 win.
Having taken out 113 to win the first set, ‘The Bullet’ swiftly won the second before being pegged back by Razma, who stole the third with a 119 checkout.
Bunting had responded well to minor setbacks throughout the match and did so again in the fourth.
Razma’s 149 out took it to a deciding leg but fan favourite Bunting held throw and sealed the victory with a 96 that ensured he finished with an average of 100.06.
“I’ve dreamt about winning this tournament for the past 20 years and I’d love to do it,” Bunting said. “With the Bunting Army behind me, who is going to stop us?”
Meanwhile, Jonny Clayton held off a valiant fightback from Daryl Gurney to take the deciding set and move into the fourth round with a 4-3 win.
Welshman Clayton edged the first set then produced checkouts of 160 and 120 to clinch the second and third respectively.
But the seventh seed faltered in the fourth and Gurney took advantage, averaging over 100 in the the next two sets to make it 3-2 before levelling the match after a somewhat comical leg, in which both players missed multiple darts at double.
Clayton came through in the decider, though, shrugging off four missed darts for the match to hit double four to set up a fourth-round tie against Gerwyn Price or Joe Cullen.
“That is my luck,” he told Sky Sports. “In games like that you need a little bit of luck. He missed a few chances and I missed a few and at 3-3 my heart started to beat big time.”