Woods, whose six-under-par 65 earned him a share of the lead after the first round, drained a four-foot birdie at the 475-yard par-four 11th to move to 7-under par.
Kevin Streelman, who also started from the 10th hole, had a blistering second nine to complete an eight-under-par 63 that put him in the clubhouse on 7-under 135.
Streelman, who just missed out of joining a playoff the last time the Barclays was held at Ridgewood Country Club, made four birdies in a row from his 12th hole and rolled in an 11-foot birdie at the last to cap off a brilliant round.
One stroke away was fellow-American Stewart Cink, who posted a 69 for a two-round total of 136.
In the clubhouse another shot back on 5-under-par 137 were Australian Adam Scott (71), Ireland's Padraig Harrington (68) and Americans Ben Crane (70), Tim Petrovic (69) and Webb Simpson (65).
Simpson birdied five of his last six holes to surge into contention at the opening event of the FedExCup playoffs.
The 121-man field was playing the ball down after being allowed to lift, clean and place on Thursday due to soggy conditions after heavy rain earlier in the week.
World No. 2 Phil Mickelson was unable to take advantage of the receptive greens and looked likely to miss the cut after shooting 74 for a 4-over-par total of 146.
However, Mickelson was assured of qualifying for the next tournament in the four-event playoffs, the Deutsche Bank Championship in Boston, based on being fourth in the standings entering the tournament.
The Barclays cut, to include the top 70 and ties, was projected to come at level par 142.
In Gleneagles, Scotland, Europe’s Ryder Cup race reached an exciting level on Friday with three of the four players battling for two places locked on the same two-round total in the Johnnie Walker Championship.
Peter Hanson and Miguel Angel Jimenez — the two currently holding the final two spots in the last event to count — and Simon Dyson, hovering just outside the automatic top nine, were on 6-under-par 138.
They were three strokes behind the halfway leaders, Britons David Lynn and Gary Boyd and French outsider Julien Guerrier, who were two shots ahead of the Gleneagles field.
Edoardo Molinari, the player aching to impress Ryder Cup captain Colin Montgomerie this week and gain one of the three wild cards, was also on six under.
Veteran Spaniard Jimenez was the first to throw down the gauntlet to those trying to steal his ninth and last position with a 4-under 68. Then Swede Hanson, a place above him in the table, caught Jimenez with birdies on the last three holes for a 69.
Hanson’s playing partner Dyson of Britain, effectively in the next place down on the table because of players either missing the event or withdrawing, birdied the last to join the 6-under party with a 70.
Dyson needs to win to have any chance of bursting into the top nine.
“I have to play the best 36 holes of my life to play in the best tournament of my life,” Dyson told reporters.
Italian Molinari could get the thumbs up for a wild card from Montgomerie if he wins or gets close to winning. Brother Francesco, with whom Edoardo won last year’s golf World Cup, is already in the team.
Edoardo is already urging Montgomerie to pick him and re-form that winning partnership.
“I promise Colin if he picks me and Francesco and I play together, we won’t lose a point,” Edoardo said.
With Francesco (70) also on the 6-under mark, brotherly love may well be tested at the weekend.
The only Ryder Cup aspirant not yet joining battle is Spaniard Alvaro Quiros, also needing a win. He trails eight shots off the lead after a 71.
Montgomerie has no on-course distractions at the weekend after missing the cut. He quickly left for his nearby home to monitor the progress of the four players in his mind for wild cards featuring in the FedEx Cup Barclays tournament in the United States: Paul Casey, Luke Donald, Padraig Harrington and Justin Rose.
