Two men and two women are tied for the lead after 54 holes at Vallda Golf and Country Club outside Gothenburg, with Drysdale in a group just one behind.
The 46-year-old from Cockburnspath followed opening rounds of 67-68 with a 70 in windy conditions to be in the hunt again for that elusive victory in his 526th start.
“The conditions were tricky with such strong winds so I’m quite pleased with that score,” said Drysdale of his day’s work.
“It was still scoreable with opportunities on the par 5s and a wee bit tidier short game would have been nice. But the greens are slow so it was difficult.”
Drysdale birdied the fourth and ninth going out, dropped his only shot of the day at the 12th before making a birdie-2 at the 15th.
“I haven’t had a lot of form of late and haven’t been playing fantastic in the build up. But in this weather it’s just survival,” he added.
“There was a little bit of a sign of some decent stuff last week.
“I’m enjoying the format and I’m looking forward to tomorrow when we’ll see what happens.”
Sweden’s Caroline Hedwall, the overnight leader, fired a 73 to get to 12 under alongside fellow LET player Alice Hewson, who birdied three of her last four holes in a 69.
The duo joined Welshman Rhys Enoch and Australian Jason Scrivener at the top after the two early starters had taken advantage of the slightly calmer conditions on a very windy day to card a pair of 66s.
English pair Ashley Chesters and James Morrison, Australian Scott Hend and Spaniard Adrian Otaegui are alongside Drysdale on 11-under.
Twenty-six players sit within five shots of the lead, with Richie Ramsay six back after a 70 that contained six birdies. Local favourite and tournament host Stenson is on four-under.
Alison Muirhead, the other Scot to make the cut, found the going tough as she had to settle for an 85, dropping her to nine-over.