Walsall’s lead at the top of the Sky Bet League Two table was cut to one point following a goalless draw at Priestfield.
Bradford are now within touching distance of the Saddlers, who could not find a way past an inspired Glenn Morris as he produced a string of excellent saves.
The hosts started the brighter of the two teams with an early Armani Little free-kick palmed away by Sam Hornby and Max Clark unable to covert the rebound.
John Coleman’s side were indebted to Morris, who made two excellent point-blank saves in a matter of moments.
The first was from Jamille Matt who was unmarked inside the box, before the 41-year-old got up quickly to deny Jamie Jellis.
Walsall, now winless in six, were denied again just before the break with Morris producing another stunning stop to deny Matt from close range.
Gillingham pressed early in the second half as Jimmy-Jay Morgan struck wide of the target before Hornby made a good stop low to his left to repel a low drive from Robbie McKenzie.
Hornby made a crucial save late on, thwarting Elliott Nevitt’s first-time effort.
