Jeev, who is playing this week on an invite, shot an even par 71 to go alongside his first round 69 to total two-under 140 for 36 holes.
Hideki Matsuyama (65-70) and Shane Lowry (65-70), two of the co-leaders after first round dropped to tied-fourth at seven-under.
Rickie Fowler has jumped to a career-best fourth in the world rankings after his fourth victory in the past nine months.
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The South African became the first player to win back-to-back Qatar Masters` titles.
Lahiri found 11 of 14 fairways and all 18 greens in regulation as he piled up eight birdies on the La Quinta Country Club course.
Golf is returning to the Olympics this August for the first time since 1904, although its inclusion has divided opinion with some players declaring it little more than an `exhibition` sport.
Asia won two singles through Lahiri, who beat Shane Lowry 2&1 and Korea's KT Kim who beat Bernd Wiesberger 3&2.
Asia hit back from a four-point deficit to tie the match 10-10 on the final day.
The 38-year-old Englishman topped the rankings in August 2012 but missed out on the 2014 European Ryder Cup team amid a downward slide which coincided with a change of coach.
The 44-year-old, who will be assisted by Liang Wen-chong of China, has already drawn out his battle plan against Team Europe.
The 37-year-old who finished fourth in the 2015 Asian Tour rankings is tipped to make the cut along with India numero uno and world ranked 40 Anirban Lahiri, who's also coached by the Bengaluru-based Divecha.
Asian Tour number one Lahiri is the only Indian featuring in top-100.
Woods, the world number one for a record total of 683 weeks who is now stunningly ranked 414th.
While Himmat was the best Indian, the other two Indians also finished in Top-10. Gaganjeet Bhullar (71) and Khalin Joshi (70) dropped to Tied-10th place.
Retirement is still far away, I only hope that I will decide it and not my body.