Walsall's position at the top of the Sky Bet League Two standings was reduced to just one point after a scoreless draw at Priestfield.
Bradford are now close to catching up with the Saddlers, who couldn't break through an exceptional performance by Glenn Morris, as he made several impressive saves.
The home team started the game more energetically, with an early Armani Little free-kick saved by Sam Hornby and Max Clark missing the chance on the rebound.
John Coleman's team relied on Morris, who made two brilliant saves in quick succession.
The first save was from Jamille Matt, who was unmarked in the box, and then the 41-year-old goalkeeper quickly denied Jamie Jellis.
Walsall, now without a win in six matches, were frustrated just before halftime, as Morris made another excellent stop to prevent Matt scoring from close range.
Gillingham pushed forward early in the second half, with Jimmy-Jay Morgan missing the target before Hornby saved well to keep out Robbie McKenzie's shot.
Hornby came up with a crucial save late in the game, stopping Elliott Nevitt's shot.