Second-round leader Ross McGowan struggled on the front nine, but came home in 3-under 32. He ended up shooting a 1-over 72 to slip into second place at minus-5.
Spanish amateur Pablo Martin-Benavides matched the low round of the day with his 5-under 66. That helped him jump into a tie for third place at 4-under-par 209 with Graeme Storm (70). Taichi Teshima is one stroke further back at minus-3.
Noren got off to a quick start with birdies on one and three at Quinta da Marinha Oitavos Golfe to move to minus-5. He stumbled to a bogey at five, but after parring the next two holes, he found himself tied for the lead.
The Swede moved out in front for the first time as he birdied the par-5 eighth.
Noren drove just in front of the short par-4 11th with an iron. He rolled a putt from the fairway to 5 feet and drained that birdie effort to get to 6 under. A three-putt bogey on the par-five 13th dropped him to minus-5.
The 24-year-old dropped in a birdie putt on the 15th and came right back with a two-putt birdie on 16 to jump to 7 under. Noren missed a 3-foot par putt at 17 and parred the last to end one clear of McGowan.
McGowan, who is playing his second event as a professional, struggled throughout his front nine. He parred the first three holes before stumbling to back-to-back bogeys from the fourth.
The Englishman continued to fall down the leaderboard as he double-bogeyed the par-5 seventh. That dropped him to minus-2, two behind the leader.
McGowan started to rebound around the turn. After a birdie on 10, he knocked in a 5-foot birdie putt at the 11th to get back to minus-4.
He carded four straight pars, but was three back of Noren. McGowan dropped in a 4-foot birdie putt on the 17th to close at 5 under, which got him one back after a Noren bogey at the same hole.
Andrew Oldcorn and Jamie Spence tied Martin-Benavides for the day's low round as they each shot 66. Those two jumped from a share of 47th into a tie for sixth at 2-under-par 211.
They were joined there by Alastair Forsyth, Raphael Jacquelin, Michael Jonzon and 1999 British Open champion Paul Lawrie.
Stephen Gallacher, Soren Hansen, Charl Schwartzel and Sven Struver were the final players in red figures at minus-1.