The 44-year-old, who has finished runner-up three times on the circuit during a career spanning 19 seasons, sits a shot off the lead in the $1.75 million event at Education City Golf Club.
With his wife Vicky caddying for him, Drysdale backed up confidence-boosting opening rounds of 67 and 69 at the new venue for the tournament with a bogey-free seven-under-par 64 for a 13-under total.
The Cockburnspath man, who is bidding to emulate both Andrew Coltart and double champion Paul Lawrie by winning this event, is in joint-second behind Spaniard Jorge Campillo, with Drysdale's compatriot, Scott Jamieson, also in the top 10 on nine-under.
"I started quite well," said Drysdale of his excellent day's work. "I birdied one and two, holed a couple of nice putts and was four-under through six holes.
"I struggled a bit in the middle of the round, but managed to move on by making some two putts from 40 to 50 feet and was able to capitalise on my good shots."
The pick of those was probably an 8-iron from 160 yards to four inches for one of very few birdies all week at the par-4 17th, where the Scot had dropped a shot on the previous two days.
"I was quite aggressive off the tee there, hitting driver whereas most guys are hitting 3-wood," he added. "I got it down to a good number and hit an 8-iron that was perfect - those are the type of birdie putts that you like."
Drysdale, who has held a full card for 16 consecutive campaigns, started strongly last season before seeing his game go off the boil. In seven events so far this season, his best effort has been a tie for 36th in the Alfred Dunhill Championship at Leopard Creek in South Africa.
"It's not been fantastic lately and it's been a case of getting the head down, trying to grind out things to try and see some improvement," admitted Drysdale.
"But I had a good couple of days with my coach, Jamie Gough (brother of former Rangers and Scotland defender Richard), on Tuesday and Wednesday and I felt really good on Thursday shooting that four-under.
"I played very solid from tee to green. It's not been quite as good since then and today was good for maybe 12 of the 18 holes. But, overall, it is going in the right direction."
The European Tour record for most attempts at landing a win is currently held by Englishman Malcolm MacKenzie, who was making his 505th appearance on the circuit when he landed the 2002 French Open.
Drysdale first came close to making the breakthrough in the 2006 Russian Open, finished second again three years later in the Andalucia Open and then once more in the Alfred Dunhill Championship in 2008.
"Swing-wise," he added of that work with Gough, "we've been working on trying to get my left shoulder behind the ball at the top of the backswing by keeping the width on the way back.
"We've played in a lot of wind lately and I tend to get left-sided. I have to get behind it to make a pass at it. If I don't, I'm in all sorts of trouble and that's been my main problem."
All 22 previous stagings of the Qatar Masters took place at Doha Golf Club, where Coltart won the inaugural event in 1998 before Lawrie landed the title the following year then again in 2012.
"I'm enjoying the greens," said Drysdale of the new venue. "You expect a lot of grain, but these aren't at all.
"It has a links feel to it. There's been no expense spared obviously, but it looks as though it could have been here for 50 years the way the fairways play. It is immaculate."
Campillo, who took 229 events to land his maiden win in last season's Trophee Hassan II in Morocco, was three clear of the field at one point after making five birdies in six holes around the turn.
A couple of bogeys left him having to settle for a 67, giving him a one shot lead over both Drysdale and Dane Jeff Winther (65).
Winther's compatriot, Benjamin Poke, sits a shot further back, with Spaniard Pablo Larrazabal on 11-under after a equalling the course record with an eight-under-par 63.
Jamieson, who started the day a shot ahead of Drysdale, was three-under for the round though 10 holes before before covering the closing stretch in one-over as he signed for a 69.
Stephen Gallacher and Bob MacIntyre both signed for 68s to sit in a tie for 28th on five-under, one better than Richie Ramsay after he was also round in three-under.