Campbell, looking for his first win in seven years, made a 15-foot par putt on the last hole to complete a round of 69 that put him at 10-under 200. Jimenez is trying to win the event for a third time in nine years.
"I wouldn't say I played well today as it was a bit scrappy and really pretty average but then I managed to grind out a score and that's important when you are not playing all that well," Campbell said.
Campbell survived a scare during his round when he accidently knocked his ball off the tee at the par-4 10th hole while taking a practice swing. However, the 2005 U.S. Open champion avoided a two-stroke penalty after a ruling that he had not addressed the ball and therefore was not in breach of the rules.
"I've never ever done that before in 38 years of playing golf and knocking the ball off the tee in taking a practice swing," he said.
Campbell, ranked at No. 339th, has won 15 career titles but none since the 2005 HSBC World MatchPlay Championship in England.
"It would be very satisfying to be standing here tomorrow night as the ... winner, given what has happened in my life and with my career the last seven years," he said.
Matteo Manassero had a 64 that moved him into a share of third place at 9 under with 47-year old Lian-wei Zhang (69) of China.
"I played well throughout the whole round so everything came together for me," said Manassero, who won the Singapore Open last week. "After winning last week that has made me more relaxed on the golf course, and my position is certainly due to what happened last week as I've got more freedom."
Sweden's Fredrik Andersson Hed (70) was another shot back, and Denmark's Anders Hansen (70) and Ireland's Peter Lawrie (67) were tied for sixth at 7 under. American Matt Kuchar (66) was among five players in eighth, four shots off the lead.