The 42 year old Englishman is playing on a sponsor's invite after losing his European Tour card last year, but looked to be returning to form as he reached 11 under with four holes to play.
Having opened with a 67 - one behind overnight leader Brandon Pieters - two-time European Tour winner Tunnicliff raced out the blocks with five consecutive birdies.
His progress was checked somewhat by bogeys at the sixth and ninth, but he retrieved those shots with further gains on the 11th and 12th.
Leading in the clubhouse were South African Branden Grace and Austrian Markus Brier - who retained his card by the skin of his teeth at last November's Qualifying School.
Grace had six birdies and two bogeys in his round of 69, while Brier joined him on ten under with an eventful 66 that included an eagle, eight birdies and three dropped shots.
Open Champion Louis Oosthuizen had charged into a share of fourth, alongside Jaco Van Zyl, helped by a chip in for birdie at the ninth and five footer two holes later as he reached six under through 11 holes - nine under overall.