Singapore's Mardan Mamat, who held the 36-hole lead, finished two shots back at 11-under-par 205 courtesy of a double-bogey at the par-3 17th. Colin Montgomerie, Thomas Levet, James Kingston and Jonathan Lomas followed at 9-under-par 207.
Hanrahan, who celebrated his 46th birthday on Saturday, was one shot off the lead to start the third round but made a move with back-to-back birdies starting at the par-4 third at Laguna National.
He stumbled with a bogey at the sixth but pulled ahead with three consecutive birdies from the ninth to reach 12 under.
Hanrahan opened a two-shot edge with a birdie at the 14th and drained an eight-foot putt for a birdie at the 15th to maintain the advantage.
The American, who has played extensively on the Asian PGA Tour, was caught immediately by Lane and Mamat following a bogey at the 16th.
Hanrahan then parred his two remaining holes to secure a share of the 54-hole lead in search of his first career victory on the European Tour.
'That was a nice birthday gift, but I'm not letting my mind race ahead anywhere,' said Hanrahan. 'It would be awesome to win but the whole key to success is one shot at a time.'
Lane, a veteran whose last European Tour title came at the 1994 Turespana Open de Baleares, collected three birdies on the front side to make the turn at 11 under.
The Englishman kept pace with Hanrahan with a three-foot birdie at the 15th and ran home a long birdie putt at the par-4 16th to move into a tie for first at 13 under.
'You never forget how to win, or that feeling, but it is very difficult,' said Lane. 'Today I went out one shot behind and shot 67 and although I'm now tied for the lead I've gone nowhere really and everybody else has moved up. You have to play well every day on this tour.'
Mamat was flawless on his round with four birdies before sending his tee shot into the water at the 17th. He walked away with a double-bogey to finish two shots back after a round of 70.
Montgomerie had a solid performance with five birdies and no bogeys for a 67 to finish four shots back.
'A good start is required tomorrow,' said Montgomerie. 'If I can get something like 3 under after four holes then it's a different ball game.'
Henrik Bjornstad came in alone in eighth place at 8-under-par 208.
Thongchai Jaidee, Peter Lawrie, Nick O'Hern, Terry Price, Wook-Soon Kang, Jose Manuel Lara, Ter-Chang Wang and Yong-Eun Yang tied for ninth place at 7- under-par 209.