Jimenez can join Hsieh Yung-yo of Taiwan as a four-time winner of the event after previous wins in 2005, 2008 and 2012, the latter seeing him become the oldest winner in European Tour history aged 48 years and 318 days.
A first round of 70 left the veteran Spaniard six shots off the lead, but five birdies in his first six holes and another on the third had Jimenez right back in contention at Hong Kong Golf Club.
However, the 49-year-old then dropped shots at the fifth, ninth and 10th - his final hole after starting at the 11th - to card a 67 and finish three under par.
"I played very well with birdies on the 12th, 13th, 14th, 16th and 17th and a birdie on number three, but then the magic stopped," Jimenez told Sky Sports.
"The greens are very fast, you have to take care. I three-putted the fifth but I am happy, I don't feel like I putted badly but it happens.
"I thought about a low score after the first few holes but you have to respect this golf course. It's not very long but you have to get the ball in place every single time and you have to be very careful with the greens because they are firm and fast."
At three under, Jimenez was three off the lead held by Wales' Stuart Manley, who hit the headlines recently by following a hole-in-one with an 11 on the next hole during the World Cup at Royal Melbourne.
Manley, who thought he had won a car for his ace before being told it was only on offer during the final round, was three under for his round with four holes to play and led by one from Germany's Alex Cejka.
Cejka had set the clubhouse target on five under after a 67, while overnight leader David Higgins was two under after adding a 74 to his opening 64. Higgins was six over par for his first 14 holes but at least birdied the 15th and 18th to repair some of the damage.