The Owls (11-3, 2-0 Atlantic 10) trailed by as many as nine, 41-32, with 10:13 left. Temple then went on an 11-2 run to tie it at 43 on Moore's jump shot with 5:59 to play.
After the game's seventh tie at 49-49 with 2:55 left in the game, Moore scored five straight to put the Owls up for good, 54-49, on a layup with 1:13 remaining.
Temple scored 10 of its 16 points off turnovers in the second half. The Owls turned the ball over just seven times and held the Billikens without a 3-pointer on seven attempts.
Scootie Randall added 10 points for the Owls, who shot just 30.6 percent from the field (19 of 62).
The Billikens (5-10, 0-2), who lost their fifth straight, shot 43.6 percent from the field (24 of 55).
Brian Conklin led Saint Louis with 11 points and 11 rebounds.