The 352nd-ranked Gonzalez had four birdies and finished with a 2-under 70 on Saturday. Fleetwood started birdie-eagle but also bogeyed the last for a 67.
Sweden's Fredrik Andersson-Hed also began birdie-eagle and finished with a 66 to trail by a stroke. Scotland's Stephen Gallacher shot a 64 for the best round of the day to tie for fourth with Austria's Bernd Wiesberger (72).
The 43-year-old Gonzalez has led from the outset on the 2014 Ryder Cup course. He's seeking to end a four-year European Tour title drought.
"After hitting the ball well the first two days from fairway to flag, my game wasn't that good today," Gonzalez said. "But I am happy to still shoot 2-under par on that course, and I am now thinking that 21-under par might be a winning score."
The 22-year-old Fleetwood is competing in just his second full season on the tour. The 277th-ranked golfer finished a career-best sixth at the 2012 South African Open.
"Overall, it felt good out there today and I hit the ball nicely. But when I did hit it bad, I managed to get myself out of trouble," Fleetwood said. "It's been a long time since I led a golf tournament going into the last round, and it couldn't be any better."
Gallacher won the Dubai Desert Classic and is looking to become the fifth player to win two European Tour events this year.
However, the 38-year-old Scot admits he's lucky to be in the field after injuring his back last weekend while washing his car.
"The greens are fantastic and it's a course where I have had a few low scores," Gallacher said.
Copyright 2013 by The Associated Press
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