Walsall extended their unbeaten league run to four games, while Luton are now without an away win in eight matches after the pair played out a stalemate.
Walsall's Ishmel Demontagnac sent a low drive wide in the 23rd minute and Luton keeper Dean Brill blocked a volley from Edrissa Sonko four minutes later.
In the 56th minute Paul McVeigh screwed a shot wide from Calvin Andrew's cross.
Tommy Mooney's effort was saved on 74 minutes before Drew Talbot drove wide and David McDermott sliced a shot wide.
Walsall: Ince, Weston, Gerrard, Dann, Fox, Hall (McDermott 63), Wrack, Sonko, Demontagnac (Taundry 83), Mooney, Ricketts.
Subs Not Used: Bossu, Roper, Deeney.
Luton: Brill, Perry, Coyne, Fojut, Jackson, Bell, Hutchison, Spring, Wilson, McVeigh (Talbot 70), Andrew.
Subs Not Used: Goodall, Currie, Keane, Grant.
Ref: Anthony Taylor (Greater Manchester).