Justin Rose, who held the lead after an opening-round 63, managed an even-par 71 to finish three shots off the lead at 8-under-par 134 along with Geoff Ogilvy.
Tiger Woods had a scare of sorts on Saturday. After struggling with the putter in the opening round, the top player in the game bogeyed four of his first seven holes to fall back to 3-over par, two strokes off the projected cut at the time.
Woods was able to buckle down, however, and climbed out of the hole with back- to-back birdies starting at the 17th to make the turn at plus 1.
'I was certainly thinking about it,' Woods said of the possibility of ending his streak of cuts made. 'It definitely crossed my mind.'
Woods continued the recovery on the front side with two consecutive birdies from the second to return to 1 under, the exact same score in which he started the round.
The 27-year-old then ran home a 30-foot putt for a birdie at the fifth before hitting a remarkable shot at the par-5 seventh.
After his approach found a bunker, Woods blasted out and watched as his ball stopped within inches of the cup. He tapped in for birdie en route to a round of 69 and a 3-under-par 139 total.
'The swing doesn't feel all that bad,' said Woods, who has now made the cut in 111 straight events. 'I just need to get a few more putts like I did today, got some momentum going and got it rolling and hopefully I can keep it going.'
Scott played the back side first at the TPC of Boston and picked up his first birdie at the par-4 13th. He hit an 8-iron approach to three feet for an eagle at the par-5 18th and ran home a 45-foot putt for an eagle at the par-5 second to jump to minus 7.
'It was kind of just a normal day out there until the 18th where I made eagle and it kind of got me going,' said Scott. 'I felt like now is the time to get right in this tournament.'
The 23-year-old birdied the fourth and hit his approach to eight feet for a birdie at the fifth to join Singh in the lead at 9 under.
Scott kept on cruising and took sole possession of first with a birdie at the par-5 seventh. He then closed with a birdie at the ninth to pad his advantage.
Scott's best finish on the PGA Tour this year was third at the Match Play Championship, but the young international phenom hasn't finished in the top-10 since.
'You can only think of two weeks out of the whole year that were good performances but there hasn't been that much more than that, to be honest,' said Scott, who won the Scandinavian Masters on the European Tour this year. 'When I've played well, I've played quite well, but most of the time I've played quite poorly.'
Singh, who has won twice this season, ran off four consecutive birdies on the front nine to vault to the top of the leaderboard at 10-under par.
The 40-year-old stumbled with a bogey on the inward half to finish at 9-under-par 133.
'All in all, I'm playing pretty solid right now,' said Singh. 'I drove the ball very well. I hit a lot of greens and made some nice putts on the front side but the putter went cold on the back.'
Darren Clarke, who won last week at the WGC-NEC Invitational, dropped his second shot inside four feet at the par-5 18th for a closing eagle. Clarke carded a second-round 68 to join Steve Flesch, K.J. Choi and Tim Herron at 7-under-par 135.
Greg Norman, Tim Petrovic and Glen Day were one shot further back at 6-under-par 136.
The 36-hole cut fell at even-par 142 with such notables as Hank Kuehne, Aaron Baddeley and British Open champion Ben Curtis missing the weekend.