The Warhawks won for the ninth time in their past 10 games to improve to 11-5 on the season, while the Cajuns fell to 8-9 overall.
It would have been ULM's first no-hitter since Ben Sheets and Lance Caraccioli combined to no-hit Louisiana College in 1998 and would have been the first nine-inning no-hitter by one pitcher since Rickey Rockett vs. Texas State in 1973.
Granier (2-0) lowered his Sun Belt leading ERA among weekend starters to 1.45 on the season. He has allowed just five runs all season long over 31 innings of work.
Caleb Knox scored the game's first run after leading off the top of the seventh inning with a double down the line in left field. He moved to second on a sacrifice bunt by Jarrett Hammond and scored on a line-drive base hit by Matt Laird to right field.
The Warhawks tacked on an insurance run in the top of the ninth after Laird led off the frame with their third straight lead-off double. A single by Jason Hicks and a walk to Les Aulds loaded the bases. Following a fielder's choice, Caleb Clowers drove home Hicks with a sacrifice fly for what proved to be the game-winning run.
Jordan Poirrier broke up Granier's no-hitter on the first pitch of the bottom of the ninth inning. The ULL cleanup hitter lined a triple into right field; he would score the Cajuns only run of the game on a sac fly by Greg Fontenot.
Judd Edwards, Knox and Laird all finished 2-for-4 on the night for the Warhawks. Aulds drew a pair of walks and had a base hit, while Rapp belted his sixth double of the season.
The Warhawks wasted a prime opportunity to score first in the top of the second inning. Edwards led off the frame with a single to right and moved over to third on a single by Knox. ULL starter Taylor Hubbell retired the next three Warhawks -- two by strikeout -- to escape the inning.
The Cajuns had just as good of a chance in their half of the third as they loaded the bases without the benefit of a hit. Granier got Mike Petello to ground into a fielder's choice to get out of the jam.
Hubbell (3-2) took the loss for the Cajuns despite striking out eight and scattering six hits over six innings of work. ULL closer Joey Satriano allowed one run on four hits over three innings.
Grainer worked out of trouble in the seventh after he issued a lead-off walk to Michael Strentz. A sacrifice bunt moved Strentz to second and pinch runner Brian Bowman then stole third. Granier struck out Jordan Bourque looking and got Ryan Leonards to fly out to right to end the inning.
The Warhawks and Cajuns continue their three-game series Saturday afternoon at 2 p.m. ULM will send sophomore left-hander Randy Zeigler (1-1, 5.23) to the bump, while La.-Lafayette will counter with junior right-hander Jordan Nicholson (1-1, 2.25).