World No.1 McIlroy went out of bounds by an inch and threw a club as a two-over-par 74 left him in danger of missing the halfway cut for a second successive tournament – and possibly losing top spot again to Luke Donald.
Drysdale, 290 places below him in the rankings, could not believe his luck as his second shot to the final hole went into the water and bounced out again.
"You could hit 1,000 balls and never have that happen," said the 37-year-old Scot, who went on to birdie the par five for a six-under 66 and a share of the lead with Ireland's Peter Lawrie.
"I don't know what it hit – maybe a fish. It was a massive break. I don't think I can say what I would have thought if I had taken six or seven there."
McIlroy's show of frustration, which could result in a European Tour fine, came as he ran up a six on the long 12th.
It was the last of four bogeys in five holes and a double bogey at the 16th was to follow. He had earlier eagled the fourth.
Having started with a 76 last May, the Northern Irishman this time said: "A bit of deja vu. Two under through seven, so it's just pretty disappointing.
"I feel like I'm playing pretty well. I just need to go out there and shoot the scores."
On the shot at the 12th, McIlroy added: "I was just trying to cut it in, trying to hold it up against the wind and just double-crossed it."
McIlroy was the highest scorer in his three-ball. Ernie Els, the man who toughened up the course two years ago, shot 68 and US-based Scot Martin Laird, runner-up at Sawgrass, had a 73 on his debut in the championship.
Lee Westwood, whose play-off defeat to Donald 12 months ago cost him the No.1 position, returned a 70.