MALELANE, 13 Dec 2014 (AFP) - Grace, who won all four of his previous European Tour titles in 2012 before going off the boil, had started the day comfortably ahead after opening rounds of 62 and 66.
But the 26-year-old had to battle hard for a third round 72 to remain on that mark, with the little-known Bjerregaard slashing his five shot overnight advantage down to one.
Winner last week in the Nedbank Challange, Danny Willett stayed in touch in third place on 14 under after a round of 67.
Ryder Cup player Francesco Molinari, who had the best round of the day on Friday with a 65, was a shot further back in fourth following a round of 70.
Grace bogeyed the long second, but swiftly birdied the third from 25 feet and picked up another shot at the next.
Another dropped shot at the sixth was again swiftly wiped out as the South African holed from 15 feet at the next.
Grace’s approach to the 11th spun back off the green and led to a bogey, but a birdie from tap-in range at the 14th following a superb pitch kept him four ahead.
However, as Grace bogeyed the 17th after missing first the fairway and then the green, Bjerregaard was storming home with a hat-trick of birdies.
Grace did well to save par at the last after his third overshot the green and narrowly escaped the water.
The 23-year-old Bjerregaard, who finished 34th on The Race to Dubai during an impressive rookie campaign last term, was only level par for the day at the turn.
However, after birdieing the tenth he holed an eight foot eagle putt at the 13th and birdied the 16th from ten feet, 17th from 15 feet, and took advantage of the long last.
Former Masters champion Charl Schwartzel’s chances of completing a hat-trick of wins in this event appear over as he carded a third round 76 to end the day 15 shots off the pace.
Third round scores on Saturday in the European Tour's Alfred Dunhill Championship, played at the par-72 Leopard Creek Golf Course:-
200 - Branden Grace (RSA) 62-66-72
201 - Lucas Bjerregaard (DEN) 68-67-66
202 - Danny Willett (ENG) 66-69-67
203 - Francesco Molinari (ITA) 68-65-70
204 - Andrew Johnston (ENG) 69-67-68
206 - Louis Oosthuizen (RSA) 69-69-68
208 - Shaun Norris (RSA) 68-67-73, Morten Madsen (DEN) 70-66-72
209 - Tjaart Van der Walt (RSA) 67-67-75, Trevor Fisher (RSA) 73-67-69, Richard Sterne (RSA) 71-71-67, Danie Van Tonder (RSA) 70-69-70
210 - David Drysdale (SCO) 71-68-71, Scott Jamieson (SCO) 68-70-72, Thomas Pieters (BEL) 71-71-68, Benjamin Hébert (FRA) 68-70-72
211 - Justin Harding (RSA) 71-70-70, Mark Murless (RSA) 71-68-72, Alex Haindl (RSA) 71-67-73, Johan Carlsson (SWE) 70-68-73
212 - Thomas Aiken (RSA) 71-72-69, Louis De Jager (RSA) 69-67-76, Christiaan Basson (RSA) 69-69-74, Jbe Kruger (RSA) 68-69-75, Jacques Blaauw (RSA) 71-68-73, Jean Hugo (RSA) 69-71-72, Craig Lee (SCO) 68-72-72, Ignacio Elvira (ESP) 67-71-74, Shiv Kapur (IND) 71-66-75, An Byeong-Hun (KOR) 71-69-72