Tyler then pulled off a superb save to prevent Brodie heading home from close range before Luton punished their opponents as Drury smashed his spot-kick past Michel Kuipers.
But the Reds keeper kept his side in the game, first thwarting Matthew Barnes-Homer before fumbling Drury's long-range volley.
Brodie restored parity after latching onto McAllister's cushioned header before lashing the ball into the back of the net.
And McAllister ensured Crawley remained above AFC Wimbledon, who beat fellow promotion hopefuls Mansfield 5-2, as deep into injury time he put Dannie Bulman's pass beyond the Hatters keeper.
Luton: Tyler, Gleeson, Murray, Kroca, Blackett, Gnakpa, Keane, George Pilkington, Drury, Barnes-Homer, Atieno (Crow 57). Subs Not Used: Kevin Pilkington, Amari Morgan-Smith, Howells, Asafu-Adjaye.
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