Last week's winner Molinari -his triumph at Gleneagles was swiftly followed by a wild card from Europe Captain Colin Montgomerie - was still to have his first bogey in the tournament.
But Jiménez followed up his scintillating career-best 61 on Friday by also going to the turn in a four under 32.
The 46 year old Spaniard, also seeking his third title of the season, turned at 18 under par, with Molinari 15 under and 17 year old fellow Italian Matteo Manassero lying third at 12 under.
Last year's British Amateur Champion Manassero is trying to become The European Tour's youngest-ever winner and after bogeys on the fourth and fifth he finished the outward half with a hat-trick of birdies.
Jiménez picked up strokes on the first, fifth, seven and eighth - and missed six foot chances at the sixth and ninth.
Molinari's three wood tee shot on the driveable par four seventh was struck to within five feet of the flag, but he missed the eagle opportunity.
Earlier Ireland's Peter Lawrie produced his lowest round on The European Tour with an eight under 63.
Having survived the halfway cut with nothing to spare at one under Lawrie, who lost a play-off for the Czech Open to Swede Peter Hanson two weeks ago, made it all the way from 61st to third, but had slipped back to fifth as the overnight leaders started for home.
Jiménez had his first bogey in 39 holes after he strayed into the trees at the 12th, but on the very next hole Molinari missed the green and dropped his first shot in 53 holes - since the 14th of his final round at the Johnnie Walker Championship.
The gap returned to three as a result and Manassero's seven foot birdie putt on the 13th meant he was now only four back in third.
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