The South African entered the day three shots off the lead but in a week where many milestones have been set at Meloneras Golf, he carded the lowest round of his European Tour career with a 63 to get to 18 under.
Higgo was five under for his first four holes to leap out in front and he would not be passed as he came home in 34 after a front nine of 29.
He is playing just his 24th event this week but already has a win to his name at last season's Open de Portugal at Royal Óbidos and secured a first top ten of the 2021 Race to Dubai last week in Austria.
"It was good," he said. "An unbelievable start, obviously.
"I wasn't playing that well, I think it's definitely the course where you can hit it off line. I putted well, my chipping has been great, so I definitely scored very well. A couple of times we were in some funny spots and I couldn't believe where I hit them.
"I'm definitely going to try and be aggressive if I can but I'm just going to enjoy it. It's a good spot to be in."
Overnight leader Thorbjørn Olesen had already been caught by the time the later groups teed off and he was soon passed as Higgo made his flying start.
The 21-year-old was dialled in with his wedges and he sandwiched an approach at the first and a tee shot at the third to 12 feet with a second shot to three feet at the second to join the lead.
Syme had carded a career best 61 on day two but he did not look like he would get near matching it when he picked up just two shots on the second and fourth to turn in 32.
But he holed his second for an eagle at the tenth and then added further gains at the 11th and 12th to also hold a share of top spot.
Higgo burst clear as, despite being in an awkward lie, he put his second at the par five fourth to two feet for an eagle to lead by two.
A two putt birdie from Syme on the 13th had him within one and while he dropped a shot on the 15th, he chipped in for a birdie at the 16th and made the most of the par five last to get back into a share.
Higgo almost drove the tenth to set up a birdie after a brilliant chip but he gave the shot back on the next before holing a 15 foot right to lefter on the 14th to lead alone once more.
Meanwhile, a fast finish from Pavon moved him alongside Syme at 16 under.
The 28-year-old had turned in 33 with two birdies and a bogey but he picked up shots on the tenth and 13th before finishing with three birdies to fly up the leaderboard.
That had him one back but Higgo got up and down on the last for a closing birdie and led by two.
Schwab had endured a frustrating day with the putter, with just birdies on the fourth and eighth to his name, but he holed his second on the 17th from around 80 yards and he was suddenly within two.
Winther carded the lowest round of his European Tour career with a 62, while Horsfield followed his 61 the previous day with a 65.
Wu Ashun's 61 was the lowest round ever recorded by a Chinese player on the European Tour and moved him to 14 under alongside Olesen, another Dane in Joachim B. Hansen, Welsh duo Jamie Donaldson and Rhys Enoch, Dutchman Wil Besseling, German Maximilian Kieffer and Italian Guido Migliozzi.