The 38-year-old, whose last top-three finish on the main circuit came at the 2012 the Joburg Open, posted a 65 to sit three shots behind the early frontrunner Ricardo Santos, who set a blistering pace with a nine-under 62.
Starting on the 10th tee, Drysdale slipped to a bogey on his opening hole but he produced a purposeful salvage operation and picked up four birdies on his outward half.
The Scot, 11th at December's Alfred Dunhill Championship in South Africa, leaked another shot on the first but picked up an eagle and two further birdies to finish among the leading pack.
Peter Whiteford opened his challenge with a 68 while Jamie McLeary, Chris Doak and Craig Lee all posted two-under 69.
Santos who had a top-10 finish here last season, reeled off nine birdies in a spectacular round, The 31-year-old from Portugal, a former winner of the Madeira Islands Open, finished the day two strokes clear of Garth Mulroy of South Africa, Welshman Rhys Davies, England's Richard Bland and Lucas Bjerregaard of Denmark.
"I made nine under in Madeira to win the event, but I shot 63 there, because the par was 72," Santos said. "Today was definitely one of my best rounds of golf so far."
Elsewhere, Catriona Matthew's 20th season on the LPGA Tour began with a two-over 74 in the first round of the ISPS Handa Women's Australian Open in Victoria.
Carly Booth, the former Ladies' Scottish Open champion, posted one-under 71 which left her five shots behind the Norwegian leader, Suzann Pettersen, who hit 66.