Williams, a former Auburn player, finished at 14-under 274 at El Bosque. He earned $112,500 to jump from 39th to fifth on the money list with $158,875. The final top 25 will earn 2013 PGA Tour cards.
Haley, the Chile Classic winner in March, shot a 68. He leads the money list with $229,834.
Scott Gutschewski had a 66 to finish third at 12 under.