The 37-year-old Spaniard, looking to end a two-year victory drought, shot a 2-under 70 to finish alongside Sweden's Carl Pettersson at 7-under-par 209 at Taiwan's Ta Shee Golf and Country Club.
Jimenez rolled in a 30-foot birdie putt at the 16th to seize the outright lead and nearly holed a putt two holes later for a closing birdie. But an easy par turned into a bogey when his concentration lapsed on the short comeback putt.
'On the second [putt] something was going through my mind and I missed it,' said Jimenez. 'Sometimes you think you are concentrating but your mind is open to anything that goes through it.'
Jimenez, whose tie for third at the British Open helped him to the 20th spot on the final 2001 Order of Merit, hasn't titled since the 1999 Volvo Masters, his sixth career win on the European Tour.
'But it is always nice to be under par and I'm hitting the ball well,' he said. 'If I can keep my concentration tomorrow I'll be there.'
Pettersson, a rookie in 2001, used a third-round 69 to move into position to capture his breakthrough title.
'It feels nice to be leading,' said Pettersson, 24. 'I've had a good year but it's been a while since I was in contention and it's nice to be playing in the last group on Sunday.'
The best of Pettersson's three top-10 finishes in 2001 was a runner-up showing at the Open de Argentina in March. He ended the season 61st on the Order of Merit and earned his playing card for 2002.
Frenchman Thomas Levet carded a 69 to finish one shot back with second-round leader Jarmo Sandelin, who shot an even-par 72. England's Brian Davis (69) and Welshman Stephen Dodd (70) were next at 5-under 211.
Thongchai Jaidee of Thailand and Korea's Charlie Wi matched 68s to join Barry Lane (69) and Jose Maria Olazabal (72) in seventh place at 4-under.
Vijay Singh, who had back-to-back victories in Asia earlier this year, finished four shots off the pace at minus-three. He posted a 1-over 73.
Seven strokes back at even-par 216 was New Zealand's Michael Campbell, the winner of the 2000 Johnnie Walker Classic on the Ta Shee Resort layout.
The BMW Asian Open, which is co-sanctioned by the European Tour and the Davidoff (Asian PGA) Tour, is the first event that counts toward the 2002 European Tour Order of Merit.
Full-Field Scores from the BMW Asian Open