Curtis carded his second successive bogey free five-under par round of 67 at the TPC San Antonio to stand at 10-under for the tournament, two strokes clear of David Mathis, who also shot 67.
"I'm playing obviously really well," Curtis said.
"The key around here is if you can drive it straight, keep it in the fairway, give yourself a chance to get at some of these pins, with the slope of the greens and stuff like that, it makes it a lot easier from the fairway. I did that.
"I hit a lot of good iron shots. Left them, for the most part, on the right level and made a few putts and, you know, it was a pretty easy round two."
The 34-year-old Curtis, winner of the 2003 British Open, is searching for his first US PGA Tour win in almost six years.
Matt Every, who set a new course record with his bogey-free 63 on Thursday, had a very different round on Friday.
He failed to make a single birdie and gave up four bogeys through 12 holes, but grabbed back two strokes with birdies on the 14th and 16th before his round was halted due to bad light.
He will finish the round early on Saturday.
Cameron Tringale made a strong move with an impressive seven-under 65, avoiding any bogeys as he took advantage of the better early conditions with less wind.
The projected cut is at four over and among those expected to miss out includes Australian Stuart Appleby, who shot 81 on Friday, 10 strokes more than he shot in the first round.
American Boo Weekley withdrew after seven holes of his second round with an illness, joining Kevin Na and Kevin Chappell on the withdrawal list.