The No. 1 player in the game fired an 8-under 64 on Friday to inch with two of Randhawa's lead.
Randhawa finished 36 holes at 10-under-par 134, with two-time U.S. Open winner Retief Goosen, who posted a 5-under 67, one back.
Woods was joined by another major champion, Michael Campbell, who carded a 2-under 70, in third place at 8-under-par 136.
'I'm right there in contention,' acknowledged Woods, who finished second in this event last year. 'There are some good names up there.'
Woods opened with three straight pars at Sheshan International Golf Club, but turned it on from there. He tapped in a three-foot birdie putt at the fourth, and followed with a seven-footer for birdie at five. He birdied the sixth and polished off four consecutive birdies with a six-footer at No. 7.
The reigning British Open winner and PGA Champion parred his final two on the front side, despite having good looks at birdie for a 4-under 32. Woods then flew out of the gate on the second nine with a five-foot birdie putt at 10 and an eight-footer for birdie at 11.
Woods got up and down from short of the green at the par-3 12th and put himself in good position for birdie at the 13th. He had 18 feet for birdie, but blew the putt almost four feet past the cup. Woods missed the comeback putt and left with a bogey to fall back to 5-under par for the championship.
Woods more than atoned for the error at 13 with a spectacular 4-iron second shot at the par-5 14th. His approach stopped six feet from the flag and he converted for an eagle.
'That was a good shot,' deadpanned Woods.
He parred his next three holes then reached the green in two at the par-5 closing hole. Woods' 25-foot eagle chance moved left at the last second and he settled for a birdie and a two-shot deficit heading to the weekend.
'It was nice to hit good shots and get the putter going,' said Woods, who has won his last six stroke-play events. 'It's nice when it comes out like this. I made the adjustments today and it paid off.'
As great as Woods was on Friday, he still trails Randhawa by two.
Randhawa struggled badly at the start of his round with bogeys at 10 and 11, his first two holes of the second round. He made up for the lost shots with back-to-back birdies at 12 and 13. Randhawa birdied the 16th to head to the second nine in 1-under 35.
Randhawa got to 9-under par for the tournament with a birdie at the third. He birdied the fifth for the second time in as many rounds, then got to minus-11 thanks to a four-foot birdie putt at seven.
He held a four-shot lead at the time, but drove into a bunker at eight. Randhawa could only blast out, then laid up at the par-5 hole. His fourth stopped 25 feet from the hole, but he could not hole the par save.
Randhawa parred the ninth to stay atop the leaderboard.
'Today, after starting with two bogeys, this was good,' said Randhawa, who is winless on the European Tour. 'I knew what I had to do. I had to stay calm and focus on the job at hand. I'm proud of myself.'
Goosen started strong with three birdies in his first four holes, but played the next 11 holes in 1-over par. He birdied his final three holes, including a three-footer at the last to get within one.
Campbell bogeyed the first, but tallied two more birdies on the front side. He parred his opening seven holes on the back nine and got to 8-under par with a five-foot birdie putt at 17.
'It wasn't good as yesterday,' said Campbell. 'I turned a 73 into a 70. I'm lucky to be here, so I'm very, very pleased.'
Padraig Harrington, who won the 2006 European Tour Order of Merit two weeks ago, shot a two-under 70 and is tied for fifth place with Chawalit Plaphol (70) and Marc Warren (71). The trio finished at minus-7.
Shiv Kapur (67) and Yong-Eun Yang (72) are tied for eighth at 6-under-par 138, one shot better than Alan McLean (68), Luke Donald (69), Jeev Milkha Singh (69), Tadahiro Takayama (67), Colin Montgomerie (70), John Bickerton (71), and world No. 2 Jim Furyk (66).