Title favourite and joint first day leader Toms had an eagle and seven birdies, but after threatening to run away with the event midway through the second round, gave the chasing pack hope with three bogeys in the last five holes to stand 10 under.
Playing partner Harrington, out in 32 after four successive birdies starting at the sixth, picked up more shots on the 12th and 17th, but the second of those widened his deficit as Toms holed from off the green for eagle.
The former US PGA champion, winner of the Sony Open in January and runner-up to Tiger Woods in last week’s Ford Championship is the only member of the world’s top 10 taking part in the event.
Harrington, lying joint third as the day’s play came to a close, is one of five Europeans who go into the weekend with hopes of toppling Toms.
Swedes Daniel Chopra and Mathias Gronberg are also on six under, Chopra after a 65 and Gronberg following a 71, while Lee Westwood and Luke Donald are one further back.
Three weeks after finishing fifth in the Nissan Open in Los Angeles Westwood added a 66 to his opening 73 and from joint 47th overnight even found himself out in front for a while.
Donald, meanwhile, played his last seven holes in a spectacular six under par for a 67.
Westwood, seeking his first victory since 2003, turned in 33 with birdies at the 10th, 12th and 14th and then had three more in a row from the fifth.
That was good, but what Donald did over the same stretch was even better.
The world number 14, second favourite for the title based on the rankings, followed birdies at the third, fourth and fifth with a 20-foot eagle putt on the next and then picked up another shot at the short eighth to be home in 30.
Last weekend Chopra was second with a round to go in Miami, but paired with Woods, crashed to a 77 and 20th place.
Toms will resume tomorrow one ahead of fellow American Billy Mayfair, while another in the group on six under is Australian Geoff Ogilvy, winner of the Accenture world match play title two weeks ago.
His 71 was almost as much of a rollercoaster as his opening 67, which had included everything from an albatross - only the second on the US Tour this season - to a double bogey.
Early in the day Ogilvy was two clear of the field with four to play, but double-bogeyed the par-three 15th, dropped another shot on the next after driving into a bunker and then jumped back into the joint lead by converting a nine-foot eagle putt at the 556-yard 17th.
Greg Owen’s second successive 71 was good enough to leave him in a tie for 22nd spot midway through the day’s play, while Brian Davis knocked five shots off his opening 76 and on three over looked to have done just enough to survive the halfway cut.
However, Ian Poulter’s bogey at the 16th left him probably needing one birdie in the final two holes to make it through.