Robert Karlsson (70), Soren Hansen (73), Martin Kaymer (72) and Rory McIlroy (69) trailed by one at 8-under 136.
A group of eight players were another shot behind, including Lee Westwood (70) and two-time champion Padraig Harrington, who birdied the last hole on The Old Course for a 71.
Westwood has played bogey-free for two days.
Only three players broke 70 in cold conditions, one on each of the three courses used for the event. Magnus Carlsson shot a 68 on the Old Course, McIlroy got his 69 at Carnoustie and Paul Broadhurst equaled that at Kingsbarns.
Brier bogeyed his first hole, the 10th, but birdied the short 11th after a 4-iron rolled to 3 feet of the cup. He made three more birdies and dropped one more shot.
The Austrian has two wins on the European Tour, including the 2006 Austrian Open.
Harrington, the British Open and PGA Championship champion, rallied in difficult conditions.
I didnt hole the putts. I played very well and didnt get rewarded, Harrington said. But I holed a 15-footer for par on the 17th and a 12-footer for birdie at the last, so I feel good.
Harrington will play the third round at Carnoustie, where he won the first of two straight British Opens.
One player unlikely to challenge for the title is Ernie Els, who shot a 76 on The Old Course after four straight bogeys from the second. Hes had five top-seven finishes in seven years at the Dunhill Links Championship.
I just dont have it this week, the South African said. Im struggling with my back a little bit. I tweaked it this morning before I teed off. In this weather, its never going to warm up. Its really stiff and tight.
Former champion Colin Montgomerie was tied for 59th after a 75 at St. Andrews.
Im not performing to any of my ability right now, Montgomerie said. Its just the consistency.
Eleven of the 13 leading golfers will play Saturday at Carnoustie, the toughest of the three courses.