Miguel Angel Jimenez posted his second 67 in as many days to move into a share of third at 8-under-par 134. He was joined there by Gary Emerson, whose 7-under 64 tied Peter Senior for the low round of the tournament.
David Griffiths, Soren Hansen, David Higgins, Steven Jeppesen and eight-time Order of Merit winner Colin Montgomerie share fifth place at minus-7.
Dyson, who was playing one group ahead of Brier, started his second round on the back nine at Fontana Golf Club and for the second day in a row parred the first five holes of the side.
The Englishman birdied both par-5s on the back nine, Nos. 15 and 18, to make the turn at 7 under. Dyson also parred the first five holes of the front nine, his second nine of the day.
Dyson sank a birdie try on the par-4 sixth, then knocked his tee shot at the par-3 seventh to 4 feet. The 28-year-old sank that short putt and closed with a two-putt birdie on the par-5 ninth to end at 10 under.
'I think I have become more confident since winning,' said Dyson, who won the Indonesia Open earlier this year. 'When you are striking the ball that well, you start taking on pins you might not have before. There was a tough pin at the second today and I just thought I'd go straight at it and I knocked it to 10 feet.
'It'll be great to be out in the final group with Markus tomorrow. I love playing in front of a big crowd and the galleries following Markus have been awesome.'
Brier also played the back nine first Friday and birdied the same three holes as he did on Thursday. Those birdies on Nos. 12, 16 and 18, helped him make the turn at 9 under.
The Austrian, who won this event twice when it was part of the Challenge Tour, stuck his approach to 4 feet at the first, his 10th. That birdie got him to 10 under, but the 38-year-old found trouble at the next.
Brier left a shot in a bunker on the par-4 second and that led to a double-bogey. He birdied the fifth to get one of those strokes back, while Dyson had tied Brier for the lead with his birdies on six and seven.
Like Dyson, Brier closed with a two-putt birdie on the par-5 ninth to end at minus-10.
'I played nicely again today and just had one hiccup, that double-bogey. The rest was good again,' Brier said. 'The hole-in-one was missing, but the rest was pretty similar. I came back from that double-bogey and that gave me confidence for Saturday.'
Senior used his 64 to move into a tie for 10th at 6-under-par 136. He was joined there by Emanuele Canonica, who carded a 66 in round two. Lee Slattery, Richard Sterne, Gregory Bourdy, Gregory Havret, Jean-Francois Lucquin, Scott Drummond and Alex Rocha are one stroke further back at minus-5.
The cut line fell at 1-over-par 143 with 73 players advancing to the final two rounds. Among those missing out on the weekend were five-time tour winner Costantino Rocca (145), 2002 Volvo PGA champion Anders Hansen (148) and Adrien Mork (146), who shot 59 on the Challenge Tour two weeks ago.