This easy win took their total points to 14 from six games after losing the previous nine.
Scott Murray had this one virtually won in the first half hour with two goals as his speed brought havoc to the Walsall defence.
His form has improved since manager Gary Johnson switched his flank. He is now his side's top scorer with nine goals.
Walsall, without an away league win since September, arrived with six changes and were soon forced into another when Jorge Leitao limped off with a hamstring injury.
Murray's first goal came on 10 minutes when he picked up a pass on the run from Stephen Brooker to drive it in first time with his right foot.
Walsall had their first chance when skipper Chris Westwood sent his header down into the turf and up over the bar.
There had been a lack of understanding between City defenders Louis Carey and Matt Heywood but they quickly established a close partnership which squeezed Walsall's attack.
With top scorer Matt Fryatt among their injured, Walsall lacked a cutting edge in the first half.
James Constable, who scored twice after replacing Fryatt against Blackpool on Saturday, hardly looked like scoring this time.
His only chance saw him break clear 30 yards out but, under pressure from Carey, he shot over the bar.
Walsall were giving up the midfield as they fell back to defend around the box and Bas Savage, a big awkward but effective figure in City's attack, always caused problems.
They were looking at him apprehensively when teenager David Cotterill swung a deep ball in from the right. As it sailed past Savage, Murray took it sweetly to sweep home.
Manager Paul Merson's half-time talk in the Walsall dressing room must have been blistering with all three substitutes now on they reacted by pressuring City for the first time.
City had to ride out a tricky 20 minutes and it was close to full-time before substitute Luke Wilkshire hit the third goal.