Echenique and Storm were tied at 130 on Monday after two rounds of international final qualifying at Sunningdale, where 96 players were competing for 10 spots in next months tournament at Turnberry.
Drysdale, Gary Orr and Branden Grace were at 131, with Rhys Davies, Raphael Jacquelin and Paul Broadhurst another stroke back.
That left six players at 133 to battle for two places.
Former U.S. Amateur champion Richie Ramsay grabbed one of the spots with a birdie at the third extra hole, and Oliver Fisher hit his approach to 2 feet for a birdie at the fourth to clinch the final spot.