A minute from the interval, with the game goalless, Kyel Reid suddenly unleashed a tremendous left-footed shot from 30 yards which screamed past home goalkeeper Richard O'Donnell.
And before Walsall's half-time instructions could turn things around, James Hanson beat the offside trap to collect a long ball from Rory McArdle and hammer home a low shot to give the Bantams a two-goal cushion which proved enough.
"We have other players in the team, like Mark Yeates, who can give us a different dimension. Here they came up to the plate," Parkinson said.
"Walsall are a good side, they play with an extra man in midfield and came into the game in the second half, so we needed every player to concentrate on the job.
"Kyel's was an outstanding strike. You won't see a better goal at any level this week. It came out of the net so quickly I thought it had hit the advertising hoardings."
However, Parkinson brushed aside any talk of promotion at this stage.
"We know we have to keep focused because this is a strong division," he said.