Aaron Baddeley posted an 8-under-par 62 to grab third place. Rory Sabbatini, Cameron Beckman and Tom Byrum are one stroke further back at minus-7.
Tway's round on the Resort Course at LaCantera Golf Club started slowly, but he caught fire around the turn. He dropped in a birdie putt at the par-3 sixth from seven feet out and followed that up with another birdie at the next.
'I had a nice shot on the par-3 to get me going,' Tway said. 'The next hole, I hit it very close, just a couple of feet from the hole.'
He nearly holed his second shot at the eighth to setup a kick-in birdie, his third straight. Tway made it four straight at the ninth when he drained a 15- footer.
The 44-year-old continued his roll on the back nine. He birdied Nos. 11 and 12 to complete his run of seven consecutive birdies around the turn. After a par at the par-3 13th, Tway got rolling again with a birdie at the par-5 14th.
However, he dropped a stroke at the next when his tee shot found trees left of the fairway. Tway, who won the Canadian Open in a playoff three weeks ago, came right back to birdie No. 16. He closed out his round with a birdie at the last.
'It was a very good day. We had a nice day to play,' said Tway, who played with Scott Verplank and Rory Sabbatini in Thursday's opening round. 'We made a lot of birdies today. I think when a group gets hot together, people feed off each other, because the other guy makes it look easy.'
Slocum got off to a flying start. He converted a birdie try at the second to begin a run of three straight birdies. Slocum later notched back-to-back birdies from the sixth to move to 5-under for his opening nine.
Around the turn, Slocum moved to 6-under with a birdie at the 11th. He again sank back-to-back birdies and grabbed a share of the lead when he sank a 20-foot birdie putt at the 16th.
'I played very well today,' said Slocum. 'I drove my ball well. I hit a lot of good iron shots and my putter was really the hot club in the bag, and I made a lot of putts and felt really good.'
Baddeley started on the back nine with a birdie at No. 10. He really caught fire shortly thereafter, as he drained a birdie on the 13th to touch off a streak of five straight birdies.
On the front nine, he birdied the first and second to get to 8-under through his first 11 holes. Baddeley settled down from there as he added another birdie and one bogey over his final seven holes.
'I got off to a good start. I drove it well today and that was key,' said Baddeley. 'If I can drive it well, then I usually shoot a good score. Down the stretch I would be lying if I didn't think of 59. There was definitely a chance.'
Loren Roberts, the defending champion, carded a 6-under-par 64. He shares eighth place with Dan Forsman, John Huston, Duffy Waldorf and Tommy Armour III.
J.L. Lewis, who won the 84 Lumber Classic of Pennsylvania last week, heads a group of players at 5-under-par 65.