Randhawa, who shared third place in 2004, played the Masters Course at Laguna National and posted seven birdies with three bogeys to move one stroke ahead of Scotland's Barry Hume.
He stands at 11-under-par 133 for his third 36-hole lead on the European Tour.
The final two rounds this weekend will be played at the tougher Masters Course, which shared hosting duties Thursday and Friday with the Classic Course.
Randhawa's positive experience in the second round should help him over the weekend, but it was a different kind of experience that had him gushing after his 68.
'[I]t is only my second year on The European Tour, but it is great to play with the great names in golf like Tiger (Woods) and Ernie (Els),' said Randhawa, a former Asian Tour Order of Merit winner.
'I played with Tiger in the HSBC and Ernie in Dubai this year and I am gaining a lot of experience because of that, and by the end of this year I should hopefully be a more rounded player.'
Randhawa will be looking to improve upon his previous finishes as a 36-hole leader after placing eighth at the 2002 Hong Kong Open and ninth at the HSBC Champions Tournament last November.
'I think the thing I have learned (playing on the European Tour) is to be more consistent in my ball striking,' he said. 'I haven't been able to do that over the last two rounds in recent tournaments but it is more of a mental battle, too. You have to stay in the present and try and do your best.'
Hume also played the Masters Course on Friday, posting five birdies and 11 pars before a double-bogey on the par-3 17th dropped him one shot behind Randhawa.
He hit the water with his tee shot on No. 17 after making back-to-back birdies and finished with a 3-under 69 to reach 10-under 134 overall.
'Although it was disappointing to finish the way I did, my golf overall has been good so I am not too worried about that,' said Hume, a full-time member of the Asian Tour.
Malaysia's Iain Steel and England's Gary Lockerbie are tied for third place at 9-under 135. Steel had the best round of the day with a 65, while Lockerbie carded a 67.
Wen-Chong Liang (72) and Peter Lawrie (70) are knotted in fifth place at 8-under 136, with first-round leader Marcus Fraser (73) one shot further back at 137.
The cut line fell at 2-under 142, with last year's runner-up Nick Dougherty (72) among 18 players who made it on the number.
Defending champion Mardan Mamat (73) is eight shots off the lead at 3 under.