Broadhurst, 46, was appointed this week as the replacement for sacked manager Paul Merson, and he will be satisfied with the way his new charges held the Shrimpers to a stalemate.
Southend had the better chances of the first half and could have been in front at the break had it not been for Walsall keeper Andy Oakes.
Admittedly, Lee Bradbury's 20-yard effort after 14 minutes was straight at him but Oakes spectacularly turned Luke Guttridge's 30-yard rocket wide on 32 minutes.
Shaun Goater, reunited with old Manchester City strike partner Bradbury, should have done better when he headed over from six yards from Kevin Maher's corner after 22 minutes with the goal at his mercy.
Southend lost Spencer Prior and Mitchell Cole to injuries but Walsall could not capatalise on the disruption to the hosts as they failed to test the home goal sufficiently.
Anthony Gerrard's flicked header was plucked out of the air by Darryl Flahavan on 17 minutes. Flahavan then saved from Walsall skipper Dean Keates three minutes before half time after the keeper had blocked Andrew Barrowman's effort.
And with five minutes injury time being played it was the Saddlers who finished the half stronger as Scott Fitzgerald's attempt was blocked by Che Wilson for a corner, and Pablo Mills headed over from the resulting Simon Osborn flag-kick.
Walsall's hopes of upping the pressure in the second half failed came to nothing as Grant Smith's wayward 30-yard effort on 46 minutes was as good as it got.
And while the match was largely fought out in the midfield, the Saddlers will be satisfied that they were able to contain their high-flying hosts for long periods.
Substitute James Lawson went close on 50 minutes when he turned Smith and forced a diving save from Oakes, but the League One leaders had to wait until eight minutes from time before Bradbury's tame 20-yard effort tested Oakes again.
Blues maintained the late pressure with a Gower free kick from the left being hammered goalward by Luke Guttridge from 35 yards, but again Oakes was up to the job on 87 minutes.
And in the last minute Shrimpers' skipper Kevin Maher, playing with a broken nose, rose to meet Lawson's centre but headed over.
But it was the Saddlers who had the last say when Keats' free kick from the right found Anthony Gerrard but Flahavan blocked his effort at the foot of the right post.