Slocum, who missed the cut in four of five previous tournaments, had eagled the par-5 second hole and added six birdies to finish 54 holes at 16-under 200.
He's trying to become the third consecutive player to make the Tucson Open his first PGA Tour victory.
Andrew Magee and second-round leader Brandel Chamblee were tied for second. Magee, the 1994 winner, fired a 65, and Chamblee, who began the round with a two-stroke lead, had a 69. He played the first 48 holes of the event without a bogey.
Chamblee barely missed a 20-foot, sloping putt for birdie on the final hole when the ball skirted the cup before breaking downhill.
Miguel Angel Jimenez was alone at 202 after a 65, with Greg Kraft, Fred Funk and David Peoples three shots off the pace.
Holding the lead proved more difficult than getting it.
Chamblee responded to various contenders with birdies on the third, seventh, eighth and 10th holes.
His approach shots found sand in front of the 10th and 13th greens.
He lofted a deft wedge shot within a foot on No. 10 and sank the putt to reach 16 under. But on No. 13 a similar blast from the bunker ran 12 feet past the hole, and Chamblee two-putted for his first bogey.
At the time, he kept a one-shot lead over Jimenez, Magee, Slocum and Peoples.
But Slocum belied his inexperience down the stretch, sinking a 10-foot putt for birdie on No. 16 to tie Chamblee and a 6-footer on No. 17 to grab the lead. Slocum then two-putted for par from 60 feet on the dangerous 18th hole, where Kraft lost position with a bogey.
Slocum reached the green on the 495-yard second hole by hitting a 2-iron 239 yards to the back and made the 15-foot putt for his eagle.
He birdied Nos. 3, 6 and 8 on the front, and birdied No. 13 ' the hole that was Chamblee's undoing ' with an 18-foot putt to get within reach.
Magee birdied No. 18 to set up his Sunday pursuit of a second Tucson title.
Full-field scores from the Touchstone Energy Tucson Open