Canizares was tied for the lead with Levi late on the back nine, but bogeyed the 17th. He and Marsh each posted matching rounds of 6-under 66 and are knotted at 10-under-par 134.
Gil Morgan and Bob Gilder shot 5-under 67 and share fourth at minus-9.
Levi tallied three birdies in his first five holes, and appeared to be cruising to the winner's circle Sunday afternoon. He bogeyed the 11th when he pulled a 7-iron, but rebounded with a 15-foot birdie putt at No. 12 to maintain a big lead.
But Canizares flew up the leaderboard, thanks to four birdies on his front nine, all from inside 6 feet. He birdied three in a row from the 14th to match Levi in the lead at 11 under par.
Canizares missed the short grass off the tee at the 17th, then failed to find the green with his second. He chipped to 10 feet, but missed his par putt to fall one back.
Levi extended the lead at the par-5 16th. He found the fairway with his drive and had 212 yards for his second. Levi hit a 3-iron to 12 feet and made the eagle putt to move three clear of Canizares.
Trouble loomed for Levi off the 17th tee. He drove in the right rough and his ball nestled down into the thick stuff. Levi hit a long shot trying to run it up to the green, but his ball plugged and he made bogey. Levi parred the 18th to preserve his two-shot lead.
'These guys are good,' said Levi, whose only win on the elder circuit came at last year's 3M Championship. 'I'm going to have to put up some numbers tomorrow.
'I'll just keep doing the things I've been doing. I've got to make putts like I have been. You've got to have guts. You've got to be careful out there. Tomorrow is the day.'
Marsh collected only one birdie on the front nine, but caught fire on the back. He birdied 10, 11, 13 and 16, then closed out his round with an 8-foot birdie putt at 18 to get within two of his first Champions Tour victory since the 1999 Tradition.
Tom Watson, who will have season-ending hip surgery on Tuesday, carded his second 4-under 68 in as many days and is part of a group tied for sixth. Jerry Pate (66), Mark McNulty (68) and Rodger Davis (71) joined Watson at 8-under-par 136.
Vicente Fernandez (66), Des Smyth (69) and Jim Ahern (68) share 10th place at minus-7.
Defending champion Larry Nelson improved from his opening-round 74 on Saturday. He shot a 3-under 69 in the second round and is part of a logjam in 49th place at 1-under-par 143.