Wallace had 12 birdies in total, but it was the Englishman's run on the last nine holes which saw him become the first male golfer in a top flight tournament to birdie every hole on either the back nine or the front nine.
Nine consecutive birdies also equals the European tour record set by James Nitties (41) in the 2019 Vic Open and Bernd Wiesberger (38) in the 2017 Maybank Championship. Wallace narrowly missed out on carding only the second 59 in European tour history.
"That was special. I didn't know that if I'd holed that bunker shot on the 18th that it would have been a 59 and I wish I had known because it might have spurred me on to make it," Wallace said.
"I knew it was a nine in a row though and I'm pleased that I'm the first to do it in a single nine. I'll always have that, which is special."
Wallace went into the third-round seven shots behind leader Nicolai Hojgaard (22), but now holds the lead at 16-under overall, one stroke ahead of Tommy Fleetwood (32) and Viktor Hovland (26).
Fleetwood hit five birdies on the front nine, but two bogeys on the back nine cancelled out his eagle on the par five 14th.
"I played good early on. I looked at the pins this morning and it looked like the pins on the front nine were more accessible than they'd been for me on the first two days," Fleetwood said.
"Played great early doors and not that I was very far away there through the middle stretch of the round but I just felt like it got a bit trickier."
Jeff Winther (35) moved up the leaderboard to fourth overall, just two strokes off Wallace, with an eight-under par round, while Hojgaard is now three strokes off the lead alongside Ewen Ferguson (27).
World number two Rory McIlroy (34) hit five birdies and an eagle for a seven-under par round, but is eight strokes off the lead going into Sunday's final round.
