Willett fired nine birdies to pull one-shot clear of South Korean duo Seukhyun Baek and YE Yang, who had set the pace earlier in the day with a blemish-free 63, while lightning in the area saw play suspended with 36 players still yet to complete their rounds.
The 27-year-old got off to a strong start with seven gains over his first 11 holes, although temporarily lost ground when he found the rough off the 12th tee and failed to get up and down to save par.
A birdie at the 14th was followed by a two-putt from 15 feet at the next to see Willett match the tournaments record lowest 36-hole score at Crans-sur-Sierre.
“I started the day very well which is good,” Willett told Sky Sports 4. “I know that doesn???t mean too much, but the feelings have been good for a while now and we got out of the blocks quickly.
“I just carried on putting the foot on the pedal and luckily came out with a 62. The rhythm was nice and I wasn???t trying to go after anything too much.
“I didn???t think about it (posting a round of 59). You forget the par is 70 around here, but it???s nice to get out there and get a low score in.”
Amateur Marcus Kinhult continued his strong start with a four-under 66 to head in to the weekend four of the pace, with fellow Swede Rikard Karlberg a further stroke back after shanking his drive and three-putting his final hole.
Overnight leader Gregory Havret had a hole-in-one and an eagle over the course of his first 18, but he struggled to make gains like that during his second round, finishing in the group on eight under that includes compatriot Raphael Jacquelin and defending champion David Lipsky.
“Overall I???m pretty happy with my round,” Lipsky told Sky Sports 4. “I got off to a rough start with a couple of early bogeys which was sloppy but then pretty solid coming in and holed some nice putts.
“Obviously I was three over and was concerned about making the cut, but I made nice some birdies and ended up making a pretty decent score.
“Getting off to a bogey on the first made me focused and got me really concentrated on the task in hand. Obviously Danny’s playing really well, but If I stick to my game plan and hole some putts I???ll be right up there.”
Tyrrell Hatton briefly held the outright lead after reaching the turn in 30, but slipped six adrift of the lead after four dropped shots over an eight hole stretch.
Despite running up a double-bogey at the par-three 13th after finding the hazard, Sergio Garcia produced a bogey-free second half of his round to stay one under for the week, with Tommy Fleetwood a further stroke behind.
The second round will resume at 6.30am UK time on Saturday morning, with the third round set to begin later in the morning.