The Cougars had missed an extra-point attempt in the second quarter and Downingtown East coach Mike Matta decided to go for the two-point conversion with 3 minutes, 43 seconds left in the game.
Lauletta - who was 8 for 15 for 100 yards, a TD toss and an interception - threw a play-action pass to wideout Tyler Kroft, giving Downingtown East a one-point lead, its first of the game.
Meanwhile, the Cougar defense held Malvern quarterback Thomas Rumer to 5-for-12 passing for 56 yards and two interceptions.
"Not our finest performance, but our best effort," Matta said.
"I'm proud of the way we persevered. We could've packed it in - I mean, they looked like they had things going their way - and we didn't."
The Cougars are on a five-game winning streak and upped their record to 5-1.
Malvern Prep is 2-3.
Two Malvern unsportsmanlike conduct penalties helped swing the game.
The first occurred after the Friars' Robert Scaramuzza rushed 2 yards for a touchdown in the fourth quarter putting Malvern ahead, 13-6.
But excessive celebration moved the ball back 15 yards and Rumer, who was holding on the kick, failed to handle the snap.
Then after Lauletta's fourth-quarter touchdown, referees called another unsportsmanlike penalty on the Friars edging the ball closer to the end zone at the 3-yard line for the two-point conversion.
"Totally unacceptable," Malvern coach Kevin Pellegrini said of the costly penalties.
"It's not what I expect of my players and I can't accept it."
The Friars jumped out to a 7-0 first-quarter lead when Rumer rushed 1 yard for a touchdown, a score that was made possible by Malvern wideout Michael Bolte's 33-yard reception earlier in the drive.
Downingtown East replied in the second quarter with aplay-action pass from Lauletta to Kroft, a foreshadowing of the two-point conversion later in the game.
The Cougars failed on the extra point.
Malvern Prep 7 0 6 0 - 13
Downingtown East 0 6 0 8 - 14
MP: Rumer 1 run (Dollfus kick)
DE: Kroft 4 pass from Lauletta (kick failed)
MP: Scaramuzza 2 run (kick failed)
DE: Lauletta 5 run (Kroft pass from Lauletta)