Vijay Singh, John Huston and Pat Perez finished one shot back in a tie for second after matching rounds of 64.
Tiger Woods, who is now one round away from matching the all-time cut streak on the PGA Tour, finished three shots off the lead at 6-under-par 66.
'I played real solid all day and kept myself out of trouble,' said Woods. 'I only missed two greens and thought I hit the ball really well all day.'
Woods started at No. 10 of the Palm course, which along with the Magnolia layout is one of two courses in rotation this week, and jumped out of the gate with a birdie at the par-5 11th.
The 27-year-old hit his second to 10 feet at the par-4 13th for the first of back-to-back birdies before adding a birdie at the 16th to move to 4 under.
On the front side, Woods birdied the par-5 first and dropped his second shot inside 12 feet at the par-4 second. The top player in the game ran home the birdie putt before parring out, putting himself in perfect position to make history yet again on Friday.
In all likelihood, Woods, who is a two-time winner of this event, will survive the 36-hole cut and in the process match Byron Nelson's record of 113 consecutive cuts made.
Pappas played the back side first at Magnolia and found a bunker with his approach to the par-5 10th but hit out to 12 feet for a birdie.
He stumbled with a bogey at the very next hole but caught fire with a 30-foot putt for a birdie at the par-3 15th. Pappas then birdied the 16th and hit a 9-iron to eight feet for a birdie at the 17th.
At the par-4 18th, Pappas hit a wedge inside three feet and converted the short birdie putt to go out at minus-4.
'That was basically the start of where I felt like I am going to shoot a good round today,' said Pappas. 'The scratchiness with the driver was a bit puzzling to that point and once I hit that good drive down 18 I felt confident with the tee ball, so I felt like a good round was coming.'
Pappas continued the run on his second nine with a birdie at the first and dropped his approach within five feet at the par-4 second for his sixth consecutive birdie.
The South African parred the third but picked up the pace again with a birdie at the fourth. Pappas then added back-to-back birdies from the sixth to hold the outright lead.
'You can never make enough birdies in this game,' said Pappas. 'It's not something I try and do. It's something that just seems to happen and not often enough.'
Singh, who is second to Woods on the money list, tallied six birdies over his first 11 holes and played his third shot inside eight feet at the par-5 14th. Singh drained the putt for a birdie and added a birdie at the par-4 17th to reach 8 under.
David Peoples, Rocco Mediate and Dan Forsman shared fifth place at 7-under-par 65.
Geoff Ogilvy, Corey Pavin, Ben Crane, Dicky Pride, Deane Pappas, Paul Azinger, Scott Verplank and John Rollins shared eighth place with Woods at minus-6.
Defending champion Bob Burns finished seven shots off the lead in a group at 2-under-par 70.