Mayfield, a walk-on freshman, threw TD passes of 42, 25 and 60 yards. He completed 21 of 30 passes.
His favorite receiver, Jace Amaro, finished with eight catches for 142 yards and a touchdown.
Williams' scores of 1 and 18 yards came in the first quarter.
Stephen F. Austin (0-2) couldn't keep up with the prolific offense of the Red Raiders (2-0). The closest the Lumberjacks were was 14-7 after 75-yard pass from wide receiver Tyler Boyd to Mike Brooks, who scampered untouched along the sideline for the score.
The start of the game was delayed about 45 minutes because of lightning in the area.
The Red Raiders offense, which scored on their first four possessions, struck the balance that first-year coach Kliff Kingsbury has been seeking. Texas Tech finished with 731 total yards, rushing for 237 and passing for 494.
Jakeem Grant put Texas Tech on the scoreboard first when Mayfield found him in the flat on the near sideline and he ran it in from 42 yards.
Amaro, who also didn't play in the second half, pulled in a 25-yard touchdown when Mayfield found him wide open over the middle at about the 15-yard line and he ran it in untouched to make it 21-7.
Bradley Marquez, who finished with 94 yards on two receptions, caught a 60-yard TD pass from Mayfield in the second quarter that helped push the lead to 45-7 at the half.
Mayfield adds a dimension to Texas Tech's offense that it hasn't had in more than a decade. He rushed for 66 yards on nine carries.
Texas Tech scored a safety early in the third quarter when Joe Minden, the Lumberjacks back-up quarterback who replaced Brady Attaway to start the second half, threw an incomplete backward pass to Jamarcus Walker in the end zone to make it 47-7 midway through the third quarter.
On the ensuing kick Carlos Thompson, a true freshman receiver, returned the ball 67 yards to set up a 5-yard score by Quinton White to put the Red Raiders up 54-7.
Minden got the only TD for the Lumberjacks in the second half, hitting Marquis Mosley on a 36-yard score midway through the fourth quarter to make it 61-13. SFA was unsuccessful in going for a two-point conversion.
Mayfield's performance in the first quarter was a carryover from his fourth-quarter performance last week in Red Raiders 41-23 win at SMU. In that game he completed 15 of 18 passes for 175 yards and two TDs. His first quarter Saturday night he completed 13 of 15 for 191 yards and two touchdowns.
Davis Webb, another true freshman, took over for the Red Raiders in the second half. His first series ended on an interception by Patrick Brown on the Lumberjacks' 4. Near the end of the third quarter he got his first TD pass, hitting Reginald Davis on a 23-yard scoring strike to put the Red Raiders up 61-7.
The Red Raiders, who got just 11 turnovers all last season to finish near the bottom of the nation's 120 Football Bowl Subdivision schools, came up with their first of the season against the Lumberjacks. A fumble recovery by Jackson Richards in the first quarter led to Williams' second score. It was the first forced fumble and recovery by the defense since 2011 against Baylor.
They got their second -- the first interception of the season -- late in the fourth quarter when Zach Winbush picked off Hunter Taylor. Winbush returned it to SFA's 10.
The 28 points by the Red Raiders in the first quarter tied for the most in an opening period. In 2005 Texas Tech got 28 points in the first quarter of an 80-21 win over Sam Houston State.