Steve Zack chipped in with 10 points and 15 rebounds for the Explorers (11-6), who defeated Temple for the first time in their last nine tries.
Quenton DeCosey and Anthony Lee paced Temple (5-11) with 21 and 19 points, respectively. Depleted by injuries, the Owls only used seven players en route to their sixth straight loss.
Trailing by eight with 1:30 left, Temple fought back to pull within two on a Dalton Pepper driving layup with 38.5 seconds remaining.
But Duren drained two free throws with 15.6 seconds left and, after Pepper threw it away on the other end, Garland made two more foul shots to seal the victory right in front of La Salle's cheering section.
The game had some extra juice to it as ESPN's College GameDay was filmed on the Palestra floor beforehand, marking the first time the pregame show has ever come to the historic gymnasium.
Fans of both schools - Temple's decked out in red, La Salle in yellow - packed the stands more than two hours before tipoff to stand behind the GameDay set, cheering back-and-forth at each other, holding signs and soaking in the atmosphere of one of the country's most famous arenas.
With the gym filled to capacity, fans were treated to a well-played, back-and-forth half that featured six ties, before La Salle scored the final 10 points to take a 36-31 lead into the halftime break.
Temple cut La Salle's lead to 46-45 with just under 13 minutes remaining but the Explorers quickly went on an 11-1 run to build their lead to 11.
Despite being so short-handed and not having the services of starting point guard Will Cummings - who was dressed but missed his third straight game with a head injury - the Owls clawed to within four on a DeCosey 3-pointer with five minutes left, setting the stage for the late-game drama.
Saturday's game was part of the Philadelphia Big 5 series, a round-robin tournament featuring five of the city's Division I programs: Temple, La Salle, Villanova, Saint Joseph's and Penn. Both the Owls and Explorers now sport 2-1 Big 5 records.
All Big 5 games used to be at played at the Palestra - the venerable, old gymnasium on Penn's campus - but in recent years teams have moved the games to their own arenas.
Temple and La Salle agreed to play Saturday's game at the Palestra for the opportunity to bring College GameDay at Philadelphia. It marked the first time the two city rivals have met at the Palestra since 1989.