Army (3-2) took a 28-13 lead midway through the third quarter on Trent Steelman's 3-yard run before the Owls (4-1) came back with four straight scores.
Wideout Wideout Joe Jones sparked the Temple rally, taking a handoff and passing to a wide-open Michael Campbell for a 24-yard touchdown with 6 minutes left in the third to make it 28-21.
Campbell also had an 8-yard TD catch on the first play of the fourth quarter to tie it at 28-28 after a critical pass interference penalty against Army on a third-and-25 play. Brown, held in check for two quarters after a sparkling first, broke loose on scoring runs of 11 and 20 yards in the fourth quarter to put Temple ahead to stay.
Pierce, the Owls' leading rusher, was scratched for the game with an ankle injury.
Army made it 28-13 after taking the second-half kickoff 74 yards in 13 plays. Steelman gained 8 yards on a fourth-and-1 play from the Temple 35 and scored on a 3-yard run as the Black Knights kept the ball on the ground.
Down but not out, the Owls then took advantage of seven penalties called against the Black Knights, regrouped, and used some trickery to rally.
Jones started by taking a handoff, running right and passing to a wide-open Campbell in the end zone for his 24-yard touchdown. Vaughn Charlton caught a 2-point conversion pass from Stewart on a throwback across the field to move Temple within 28-21.
Soon after, with Temple facing a third-and-25 near midfield, Army's Antuan Aaron was called for pass interference against Campbell, giving the Owls a first down at the Army 32. Three plays later, Chester Stewart hit a diving Campbell at the right pylon for a touchdown.
Brown, just 5-foot-5 and 170 pounds, repeatedly outran the Army defense inside and out. After Stewart hit Campbell for a 48-yard gain, Brown scored on an 11-yard run to give Temple a 35-28 lead with 6:46 left.
Brown added a 20-yard touchdown run with 4:20 to go, reversing his field and running straight up the gut of the Army defense.
Temple's rally spoiled a stellar day for Steelman, who helped Army to what had seemed to be a commanding lead. Army scored first, taking advantage of a Temple fumble on the game's opening kickoff. After gaining 19 yards on a tricky option play, Steelman scored on a 2-yard run for a 7-0 lead.
Brown had 108 yards rushing on just seven carries and scored twice in the first quarter, but he failed to gain anything on four carries in the second as the Army defense clamped down.
A booming 69-yard punt by Jonathan Bulls pinned Temple at its own 1 late in the second. After Brown was nearly tackled for a safety, Stewart threw two straight incompletions and Josh Jackson returned Jeff Wathne's punt to the Temple 31.
Steelman quickly took advantage, rolling left on first down and hitting a wide-open Barr for a touchdown and a 21-13 Black Knights lead at halftime.