After 36 holes of regular stroke play on Thursday and Friday, the action turned to knockout on Saturday, with the top 64 from days one and two facing each other over nine holes of stroke play.
Englishman Heath had finished one shot behind leader Jorge Campillo after the first two days, with Scot Drysdale six strokes further back, but they both won three matches on Saturday to make the last eight.
Heath had made just one cut all season when he arrived in Belgium but after his heroics in the stroke play, he beat Zimbabwean Scott Vincent in the last 64 and birdied four of his last five while taking advantage of a Scott Fernandez double-bogey on the final hole to make the last 16.
There he faced Robert Karlsson and the Swede bogeyed the last and the second play-off hole to send Heath through, despite the 35-year-old playing the 11 holes in one over par.
"It will be good," Heath told europeantour.com. "Obviously big home favourite, only Belgian guy left in. But honestly, you've got to imagine that the expectations are quite low of me beating him because he's in good form."
Both men played the nine holes in level par and made a birdie on the first extra hole, with a second birdie from Drysdale sending him through after a poor chip saw Geary only make par.
Drysdale will next face Frenchman Victor Perez, while the other quarterfinals see an all-French clash between Benjamin Hebert and Mike Lorenzo-Vera, and Spaniards Campillo and Adrian Otaegui go head-to-head.