Brier completed 54 holes at 6-under-par 207 and is one stroke clear of Scott Hend. The Australian carded a 1-under 70 to move into solo second at minus- 5.
Andrew McLardy matched Brier's 67 and that helped him climb into third place at 4-under-par 209.
Second-round leader Raphael Jacquelin stumbled to a 4-over 75. That dropped him into a share of fourth at minus-3. He was joined there by Richard Sterne (69) and Graeme McDowell (70).
During the round, five separate players had at least a share of the lead at Shanghai Silport Golf Club.
With Hend and Anders Romero battling for the lead on the back nine, Brier flew up the leaderboard to claim the top spot.
Brier tripped to a bogey on the first, but reclaimed that lost stroke with a birdie on the third. He moved to minus-3 with a birdie on the eighth.
Around the turn, Brier bogeyed the 10th before a birdie on 11. He bogeyed the par-4 12th for the third straight round, but responded for the second day in a row with a birdie on 13.
'With the 12th, I have bogeyed it all three days so far, but from then on I feel comfortable with the tee shots and if you hit good tee shots it is short irons and wedges in,' Brier stated. 'You have to hit it on the fairway. I missed it on the 10th and 12th holes and was just in the thick stuff.'
Brier caught fire down the stretch. He collected a birdie at the par-4 16th and came right back with a birdie on 17 to grab the lead at minus-5. Brier closed with a birdie at the last to end one clear of Hend. Brier's final three birdies all came from inside 6 feet.
'(Sunday) that will be the key, hit the fairway and hopefully have as strong a finish as today,' said Brier of his thoughts on the final round. 'Like last year in Fontana, I had a good finish and I hope I can do the same.'
Hend birdied the fourth after three straight pars to open his round. He was tied for the lead after parring the fifth as Jacquelin dropped a shot at the fourth. Hend dropped shots on six and seven to slide to minus-3.
The 33-year-old got one shot back with a birdie at the eighth, but faltered to another bogey on nine. Hend atoned for that error with a birdie at the 11th. He gave another stroke back as he bogeyed No. 12.
Hend moved within one of Brier as he birdied the 14th. Hend carded his final birdie on 16 to get to 5 under. He parred the final two to finish one back.
Jacquelin fell out of the lead with three bogeys over his opening six holes. He went on to pick up another bogey on the back nine as he failed to card a single birdie on the day.
Adam Blyth, who was paired with Jacquelin, was even-par through eight holes and was tied for the lead with Romero. However, Blyth went 5 over par on the back nine to tumble down the leaderboard.
Romero, playing with Hend in the penultimate twosome, ran off three straight birdies from the seventh to grab the lead at minus-6. He fell down the leaderboard around the turn with four bogeys in a six-hole span.
Romero ended up carding a 2-over 73 that dropped him from third to seventh. He is alone there at 2-under-par 211. David Griffiths, Jean-Francois Lucquin and Peter O'Malley are the final three players in red figures at minus-one.
Blyth is tied for 11th place at even-par 213 with Michael Jonzon, James Kingston, Peter Lawrie and Robert-Jan Derksen.