Marshall hit back from dropping four shots on the first end of the second set, turning around a 5-2 deficit to secure the win.
Scots are therefore assured of an interest in each semi-final with Marshall's victory setting up a mouthwatering quarter-final head-to-head against his pairs partner Paul Foster this afternoon, with the winner of that match then taking on Jonathan Ross or Mervyn King in the last four. In the top half, defending champion Stewart Anderson and Darren Burnett also go head-to-head, with Andy Thomson or Rob Paxton providing the semi-final opposition.
Foster, who beat Danny Dennison, a qualifier from Torquay, 9-2, 9-3, was clinical in his dispatches, executing all shots with confidence and precision and dropped only five singles throughout.
A relaxed Foster said: "I was more than happy with my form today: 95% of my first bowls were on the button and that helped to set up good solid heads. Danny was a qualifier but you can't afford to underestimate anyone in this event. It [paying the price for underestimating an opponent] has happened to me before and I'd like to think I learned from that.
"He played well but I was always in the target area at the crucial times and always felt in control."
Thomson, a three-time winner of the event, most recently two years ago, also remains a contender, after coming from behind to beat the in-form John Price from Wales 4-7, 10-2, 2-1. In the shoot-out, Price inadvertently moved the jack away from his holding shot to lose the first end and, though he recovered to take the second, Thomson played the match-winning bowl on the third.
Katherine Rednall, an 18-year-old schoolgirl, produced a sensational display to win the women's matchplay title, totally dominating against the 24-year-old holder Rebecca Field. Ipswich-based Rednall showed maturity beyond her years as she became the youngest winner of the title with a 14-4, 11-3 triumph.