Stuart Davis of England shot 67 to trail Levet, who stands at 14-under 202 at the PGA Golf de Catalunya course. Defending champion Peter Lawrie (71) was three shots behind the leader.
Stephen Dodd (69) of Wales and Fabrizio Zanotti of Paraguay (66) were 9 under.
Levet, the overnight leader, had a four-shot lead before bogeying the short par-4 16th.
John Daly, who is serving a six-month suspension from the PGA Tour, shot 74 to drop into 51st.
Two double bogeys over the back nine seemed to deflate Dalys momentum after the former British Open champion made the turn at 2 under.
Still, Daly was pleased with his game in his first tournament since December.
I love the way I am swinging, he said. Im hitting it solid and Ive made only three bad swings, which is good coming back. Im just not making any putts, and Ive got to get that sorted out.