The game was delayed by a power outage that lasted almost two hours.
Braxton Bearden returned the opening kickoff 98 yards to give Stephen F. Austin first-and-goal at the Houston Baptist 2 on its opening possession and Johnston scored on the first play from scrimmage.
Johnson got the Lumberjacks back in Houston Baptist territory with a 37-yard run to the Huskies 41 and a play later Conque found Aaron Thomas with a 36-yard scoring pass to make it 14-0.
Stephen F. Austin (5-2, 2-1 Southland) led 31-13 at halftime and never looked back.
Houston Baptist is 1-6, 0-1.
Johnson became the second-leading career rusher in school history, gaining 133 yards on 17 carries, giving him 986 yards on 116 carries this season.