Neil Cheetham, Titch Moore, Stephen Scahill and Mads Vibe-Hastrup share second place at 4-under-par 67.
The first round, which featured strong winds, was suspended for darkness with 15 players still needing to complete their rounds. They will return to finish Friday morning.
Brier parred his first four holes, then dropped a shot at the par-4 fifth. He rebounded from that miscue at six when his 6-iron stopped 5 feet from the hole. Brier birdied his next two to make the turn at 2 under par.
At the 10th, Brier knocked a 5-iron inside a foot for a tap-in birdie. He made it two in a row at 11, then parred his next three. Brier hit a 4-iron to 2 feet to set up a birdie at 15, then the 36-year-old birdied 16 for his 65.
'I thought that it wasn't playing too easy today, but I managed to keep the ball in play and hit a few really good irons where I left it stiff,' said Brier. 'I just made one bogey, the rest was solid and when I had chances I made them.'
Cheetham had by far the strangest ride to second place. He tallied one birdie and three bogeys, but eagled three of the four par-5s, all from inside 12 feet, on the Quinta da Marinha Oitavos Golfe track.
Moore mixed an eagle, four birdies and two bogeys for his share of second place.
Scahill began on the second nine and collected four birdies in his first seven holes. He had his only hiccups of the round at one and two, both bogeys, but the 35-year-old closed with birdies at seven and eight.
Vibe-Hastrup recorded seven birdies and three bogeys on Thursday.
Paul Broadhurst, Stephen Dodd, Barry Lane and Jonathan Lomas are tied for sixth place at 3-under-par 68.
Miguel Angel Jimenez, the 2004 winner, is not on hand to defend his title. He is in the BellSouth Classic field on the PGA Tour as he prepares for next week's Masters.