The defending champions in men's double sculls, however, failed to reach the finals.
Despite dominating the event throughout his career, Drysdale missed out on a single sculls gold medal at the Beijing Olympics. He finished third behind Norway's Olaf Tufte and the Czech Republic's Ondrej Synek.
All three of the medal winners from 2008 will be in the semifinals.
Drysdale was timed in 6:54.86 over the 2,000-meter course. Synek also was a heat winner in 6:53.32. Tufte barely made it into the semifinals with a third-place finish in the heat won by Synek.
The fastest time in the quarterfinals was turned in by Alan Campbell of Britain, who finished second behind Drysdale at the 2009 world championships. Campbell traveled the course in 6:52.10.
The semifinals will be held on Wednesday and the final on Friday.
In the men's double sculls, 2008 gold medalists David Crawshaw and Scott Brennan of Australia missed out on a chance to defend their title when they finished fifth in their semifinal heat.
Crawshaw and Brennan struggled in their original qualifying heat on Saturday, finishing fourth, and had to go through a repechage race just to get a spot in the semifinals.
Ariel Suarez and Cristian Rosso of Argentina had the fastest semifinal time of 6:19.40. Luka Spik and Iztok Cop of Slovenia, who finished sixth in the 2008 finals, won the other heat.
Kim Crow of Australia had the best time in the women's single sculls quarterfinals with a 7:34.29. American Generva Stone reached the semifinals by finishing second in her heat with the sixth fastest time overall.
In the women's double sculls repechage, Wang Min and Zhu Weiwei of China earned a spot in the finals, as did Americans Margot Shumway and Sarah Trowbridge.
Rowing finals begin Wednesday with gold medals being awarded in women's pairs, women's quadruple sculls and the men's eights.
Notable deaths of 2014 [PHOTOS]