Leonard shot 3-under-par 68 in the third round to move to 16-under 197 entering the final round at La Cantera Golf Club in San Antonio.
Leonard leads Matt Kuchar by two strokes. The 23-year-old Kuchar fired a 7-under 65 to earn a spot in Sundays final group.
Leonard and Kuchar are both past U.S. Amateur champions, Leonard winning in 1992 and Kuchar in 97.
Carl Paulson is three of the pace after a 68. Marco Dawson (70), Tom Scherrer (67) and J.J. Henry (68) are five back at 11-under.
Dawson aced the 122-yard, par-3 13th, when his tee shot flew right into the hole. However, he followed that with a bogey at the par-5 14th.
Jesper Parnevik made his way to 12-under Saturday, but double bogeyed the par-4 15th and bogeyed the par-4 16th to shoot 71 and finish 54 holes at 9-under.
Leonard started the third round with a three-stroke lead over Dawson and Paulson, and played his first nine holes in even par to remain at 13-under.
The Dallas native picked up steam on the back nine, birdieing Nos. 10, 12 and 14 to jump to 16-under for the tournament. The defending champion completed his round with four straight pars.
'There are a lot of motivating factors, but too many to list,' said Leonard, who at 39th on the money list is trying to get insdie the top 30 and earn a spot in the $5 million Tour Championship.
Kuchars 64 was the low round of the day. The former Georgia Tech star started his day with a birdie at the first and then added three straight on holes 6-8. Kuchar carded three more birdies on the back nine to conclude a bogey-free round.
'Like Tiger says, 'You can only give yourself a chance,' and I've done that,' Kuchar said.
This is the 71st playing of the Texas Open. In its history, only Arnold Palmer (1960-62) and Bill Mehlhorn (1928-29) have successfully defended their titles.
Full-field scores from the Texas Open