With 51 seconds remaining and the game tied at 55-55, Lofton missed a shot in the paint, got his own rebound, shot and again got the rebound before being fouled on his third shot attempt.
"I told myself that I had to make them to put us up," said Lofton, who calmly sank the first shot.
Brady then called a time-out in an attempt to "ice" Lofton but the strategy failed.
"The coaches told me to just relax and make them like you do in practice," said Lofton who then sank the second free throw.
"He's going to get fouled because of the position that he plays, so we work on free throw with him a lot," said Grant.
With the Wildcats up 57-55, the Aztecs had an opportunity to match as Josh Zazulia was fouled with 42 seconds remaining.
Zazulia, who led Palm Desert with 18 points, missed the front end of a one-plus-one and Brawley got the rebound.
The Wildcats tried to use up as much of the shot clock as possible before Mark Rivera hit Lofton with a no-look shovel pass with Lofton scoring to extend the Brawley lead to 59-55.
Zazulia then tried a three-point shot that Lofton rebounded. Lofton was fouled immediately and sank the second of his two free throws to seal the Aztecs' fate.
Actually, Lofton's return to floor after sitting out the last five minutes of the third quarter spelled doom for Palm Desert.
"I went up for a shot and I came down a defender's foot and rolled my ankle," said Lofton.
With Lofton on the bench, the Aztecs went from a 35-34 deficit to a 43-37 lead at the end of the third quarter.
Lofton opened the fourth quarter by grabbing a rebound and scoring to cut the lead to 43-39. Rivera hit two free throws to make it 45-41 followed a Lofton jumper to make it 46-43 Palm Desert.
Miguel Melendrez and Lofton both hit jumpers to bring Brawley to within 48-47.
The Wildcats then were given a golden opportunity to take the lead when Palm Desert was called for a technical foul. However, Brawley failed to convert either of the two free throws or get any points off its next possession.
With 3:40 to go Brawley regained the lead at 49-48 when Carlos Corral hit Rivera cutting to the basket against the trapping Aztecs.
"Coach told us not to rush it so I didn't," said Corral. "Mark energizes me and gives me a boost and he's reliable so he and Lofton are always my first looks."
Corral then passed to both Melendrez and Rivera to increase the Wildcat lead to 53-50. Palm Desert scored to close to 53-52 before Melendrez hit a clutch fade-away jumper to get Brawley up 55-52.
The Aztecs then hit a three-pointer to tie the game at 55-55 before Lofton's last-minute heroics.
Lofton had 20 points to lead all scorers and he led the Wildcats with 10 rebounds.
Rivera, who had two first- quarter treys, scored 16 points and along with Corral had eight assists. Melendrez was in double figures with 12 points.
Brawley (7-5) will host Vincent Memorial at 7 p.m. Tuesday.