Nick Faldo, whose last victory on the European Tour came at the 1994 Alfred Dunhill Open, posted a 65 to share fourth place with Thomas Bjorn, David Howell and Thammanoon Srirot at 9-under-par 201.
Harrington was four shots behind Jimenez to start the day at Hong Kong Golf Club and collected a pair of early birdies while his Ryder Cup teammate stumbled from the top of the leaderboard.
Jimenez picked up a quick birdie at the first, but struggled with three bogeys over his next five holes. The Spaniard dropped another shot at the ninth but recovered with an eagle at the par-5 12th to cling to a share of the lead.
'It was a very hard day,' said Jimenez, who managed a 71 on Saturday. 'I didn't hit it properly and couldn't find the hole, that was what happened the whole day.'
Harrington found trouble with a bogey at the par-3 eighth but countered with a birdie at the par-4 10th. He added another birdie at the 12th but gave that shot back with a bogey at the par-4 16th.
The Irishman then birdied the par-4 18th to secure a piece of the lead with one round to play.
'I'm not going to be running to the range to fix anything,' said Harrington. 'I'll get a bit of rest between now and tomorrow, hit a few shots and do a few things.'
While Harrington and Jimenez exchanged shots throughout the day, Kingston came from way back to join the logjam atop the leaderboard.
The South African ran off three consecutive birdies starting at the par-3 second and tallied a birdie at the par-3 eighth to move to 6 under. Kingston then birdied the 10th but stumbled to a bogey at the very next hole.
The 39-year-old answered with a birdie at the 13th and closed his round with three straight birdies from the 16th to complete a blistering 62.
First-round leader Adam Groom finished alongside Gregory Havret at 8-under-par 202. Louis Oosthuizen followed at 6-under-par 204.
Charl Schwartzel, Alessandro Tadini and Bryan Saltus were five shots off the pace at 5-under-par 205.