The former QPR man netted in the fourth minute to leave the Hatters without a win in 13 games in all competitions and still to record a victory in ten games under new boss Mick Harford.
Luton were slow to get out of the traps and almost fell behind in the second minute when Keith Keane had to clear Anthony Gerrard's shot off the line after Lee Holmes' cross from the right.
Kevin Betsy then pulled a 20-yard shot wide before the visitors took the lead in the fourth minute when Moore was first to react to a long pass from the back, touching past the advancing Dean Brill and seeing the ball trickle into the empty net.
The Hatters responded in the 12th minute as Matt Spring crossed for Keane to see a header blocked on the line by Ian Roper before Paul McVeigh blasted the follow-up wide.
With the Saddlers happy to sit on their lead, Luton fashioned another half-chance in the 32nd minute when Drew Talbot's driving run down the right allowed McVeigh to cross for Stephen O'Leary, who mis-hit his eight-yard volley straight at Clayton Ince.
That was the best of the action on offer as both sides contrived to allow the game to splutter to the interval.
The second half wasn't much better as the visitors again comfortably soaked up what little the hosts could conjure up in the final third.
Talbot saw a diving header hit the side-netting after a Morgan corner in the 52nd minute and Spring sent a 25-yarder over the bar ten minutes later.
Luton reshuffled by bringing on Calvin Andrew then Sam Parkin and Alan Goodall.
But Goodall's first contribution was to mis-control the ball to Mooney in the 72nd minute allowing the former Watford man to send a 25-yard lob on to the roof of the net.
Mooney dragged a cross-shot wide in the 80th minute before Holmes worked Brill with a 12-yard shot a minute later.
Spring had a 30-yarder tipped over by Ince in the 81st minute and from the midfielder's resulting corner, substitute Calvin Andrew nodded in from close range only to have the goal disallowed for a push.