The 24-year-old, who finished 11th and ninth in his opening two events, has now broken par in eight of his 10 rounds since returning to the top circuit after graduating from the Challenge Tour last season.
It follow his three-under-par 68 on the Firethorn Course at Randpark Golf Club, which backed up an equally-impressive 66 on Thursday on the Bushwillow Course.
On eight-under-par, Syme sits joint-11th heading into the weekend, just three shots off the lead, held by Tapio Pulkkanen after the Finn carded an eagle and 10 birdies in opening efforts of 65 and 66.
Syme, who narrowly failed to hang on to his card as a rookie in 2018, was level-par 12 holes before transforming his round with a burst that secured birdies at the 13th, 14th and 16th.
The good day's work coincided with him winning the 2019 European Challenge Tour Shot of the Year for his recovery shot at the par-3 second hole at the Andalucía - Costa del Sol Match Play 9.
The 2019 Turkish Airlines Challenge winner showed a deft touch around the green at the innovative event at Valle Romano Golf.
Short of the green at the bottom of a bank, he produced a touch of a magic, using the contours to his advantage to pitch the ball into the side of the bank and see it run down onto the green to finish four feet from the hole.
The impressive shot received 33 per cent of the vote, beating Marcel Schneider’s hole-out eagle from the fifth fairway at the Challenge Tour Grand Final, as the German finished second with 21 per cent.
Pulkkanen, who is in his third season on the main tour, leads by one from a England's Sam Horsfield and a four-strong South African posse of 18-year-old amateur Jayden Trey Schaper, Thriston Lawrence, Jaco Ahlers and Trevor Fisher jnr.
Defending champion Louis Oosthuizen is alongside Syme after rounds of 65-69, with former Dunhill Links winner Branden Grace also luriking ominously on the same mark.
However, former Masters champion Charl Schwartzel made an early exit as he was unable to repair the damage caused by a front nine of 40 in his opening round.
Marc Warren was the only other Scot to make the cut, carding an eagle and five birdies in a 68 to sit joint-59th on four-under
In just his second European Tour event, Daniel Young agonisingly missed out by a shot after dropping after dropping two shots in the final three holes, having been three-under for the day up to that point.
There were also early exits for David Drysdale (two-under), Doug McGuigan (two-under), David Law (one-over), Craig Howie (three-over) and Ewen Ferguson (four-over).