City's opening two league matches had produced an incredible tally of 15 goals, with a 7-1 home defeat by Colchester followed by a 5-2 victory over Wycombe.
There were no such thrills and spills this time around with the Saddlers turning in a determined defensive performance to return to the Midlands with a well-earned point.
Norwich, with two straight league wins behind them, thought they were heading for a third after 62 minutes when big defender Michael Nelson powered home a header from a Paul McVeigh corner. But referee Russell Booth had spotted some pushing and awarded a free-kick, much to the disgust of new City boss Paul Lambert.
After a dull first half the home side had much the better of it after the break and had Walsall on the back foot for much of the time, but although Simon Lappin and Cody McDonald went close they could find no way through with on-loan Manchester City defender Clayton McDonald absolutely outstanding.
At the other end, Walsall had their moments, mainly in the first half, and might have gone in at half-time ahead had Darren Byfield not planted a free header wide after 35 minutes after a fine cross from Walsall skipper Dwayne Mattis.