LA Tech improves to 11-10 on the year and 3-3 in the WAC while FS drops to 9-13 and 1-5 in conference play.
Fresno State scored the first four points of the game before a free throw from Gibson finally put Tech on the scoreboard two and a half minutes into the contest.
A layup from senior forward Romario Souza at the 14:13 mark was LA Tech's first basket of the game.
Senior guard Trevor Gaskins' three-pointer from the left-corner gave Tech their first lead of the game 8-6 with 13:24 remaining until halftime.
A three-point basket from Fresno State's Kevin Olekaibe put LA Tech down four with just over seven minutes to play in the first half.
The rest of the period saw Tech outscore FS 17-5 to take a 29-21 lead into halftime. Sophomore guard Cordarius Johnson and McNeail combined to score 10 of the Bulldogs final 17 points of the half with five points apiece.
After scoring the final point of the first half, the California-based Bulldogs scored the first nine-points of in the second half for a 10-0 run to take a 30-29 lead.
Tech responded with a 14-3 run of their own over the next 5:09 as Souza scored six of Tech's points.
A fastbreak layup from Fresno's Tyler Johnson cut Tech's advantage to 50-46 with just over seven minutes remaining in the game.
Junior forward J.L. Lewis made a free throw to give Tech a seven lead with 4:07 left on the clock. Fresno State scored seven consecutive points over the next three and a half minutes to tie the game at 56-56.
Souza made 1-of-2 free throws on the following possession to put LA Tech up by one with just over 24 seconds left on the clock.
Two free throws with over 17 seconds remaining gave the California-based Bulldogs a 57-56 advantage.
McNeail missed a layup with less than nine second on the clock but the ball went out-of-bounds off a Fresno player to keep the ball with Tech.
The ensuing inbound pass was underthrown and picked off by a Fresno State player but Gibson was able to grab onto the ball and force a jump ball call that kept the possession in Tech's favor.
Gibson received the next ball on the inbounds play, drove down the left side of the lane and powered home a layup at the buzzer to give LA Tech the victory.
Johnson led Tech with 16 points while Gaskins and Souza each scored 11 points.
Gaskins and McNeail had a team-high three assists as Lewis pulled down a game-best 10 rebounds.
As a team, the Bulldogs shot 38.8 percent (19-49) from the field with seven of their field goals coming from beyond the arc. They also made 14 of their 19 free throw attempts.
Fresno State was led by Olekaibe's game-high 20 points as Garret Johnson and Tyler Johnson scored 11 and 10 points, respectively.
Jerry Brown grabbed eight rebounds and Steven Sheep dished out a game-best four assists.
The California-based Bulldogs made 41.5 percent (22-53) of the field goal attempts and 80.0 percent (12-15) from the charity stripe.
Louisiana Tech host Nevada at 7 p.m. Saturday night in the TAC.