Conners, whose only PGA title came at the 2019 Texas Open, fired a bogey-free eight-under par 64 at The Oaks course in San Anotnio with American Patrick Rodgers second on 66 after 18 holes.
The opening round was halted by darkness on Thursday with about half the field unable to finish after play was delayed by more than three hours due to thick early fog.
Conners birdied the fifth hole, reeled off three consecutive birdies starting at the par-5 eighth, then had back-to-back birdies at the par-5 14th and par-4 15th and again at 17 and the par-5 18th.
Americans Peter Malnati, Chris Kirk and Hayden Buckley shared third on 67 with a pack on 68 including four who finished play Thursday - American Matt Kuchar, Ireland's Padraig Harrington, South African M.J. Daffue and Mexico's Roberto Diaz.
