Albion bounced back from the shock of falling behind to a fourth minute goal from Villa skipper Olof Mellberg to secure a point thanks to Clement's 38th minute header.
Villa, who had opened the season with an impressive 2-0 win against Southampton, were given a severe examination by Premiership new boys Albion - particularly in the second period which they spent mostly in their own half.
Gary Megson's side created enough chances to have secured their first win against Villa for almost 20 years.
But some poor finishing and two impressive saves by Danish international goalkeeper Thomas Sorensen helped David O'Leary's Villa side hold on for a point.
Villa made a dream start when Thomas Hitzlsperger's right-wing free-kick caused chaos in the Albion area.
Goalkeeper Russell Hoult left his line to try and punch the centre clear but he never got anywhere near the ball and his unprotected net left an inviting target for Mellberg to head Villa into the lead.
The shock of falling behind so soon rocked Albion back on their heels and Villa went on to enjoy their best spell of the match.
Carlton Cole shot just wide in the eighth minute with Hoult denying Gareth Barry after 18 minutes.
But Albion had a major let-off 60 seconds later when Mellberg once again made his presence felt in the air.
He rose to meet a corner from Nolberto Solano and his header was only half-saved by Hoult.
Albion left-back Paul Robinson then completed the clearance but the ball looked to have crossed the line.
The decision not to award a goal left the Villa players fuming - especially as television replays later showed the ball was clearly over the line.
It was a let-off that Albion grabbed with both hands as they finally managed to force their way into the game.
Clement whistled a free-kick just wide before Geoff Horsfield was guilty of a glaring miss.
His close-range 24th minute shot was beaten away by Sorensen after good work by Kanu.
But Sorensen was powerless to prevent Clement earning Albion a reward for their good spell when they drew level seven minutes before half-time.
Just as Villa had opened the scoring from a free-kick, Albion equalised from a training ground set-piece.
Jonathan Greening floated in a free-kick from the right-hand side of the Villa area.
Clement found himself unmarked and his 14-yard header whistled into the back of the net past a bemused Sorensen - adding to the goal he scored in the 1-1 draw at Blackburn Rovers last weekend.
The former Chelsea defender almost repeated the feat on the stroke of half time when he headed a Greening corner inches over the bar.
Clement proved to be a thorn in Villa's side and it needed another smart save by Sorensen in then 53rd minute to prevent him giving Albion the lead.
After Horsfield had been fouled 20 yards out by Martin Laursen, Clement fired in a free-kick that Sorensen had to spectacularly fly to his left to push away for a corner.
Albion were in the ascendancy at this stage and Darren Purse twice went close to giving them the lead with two headers in the space of three minutes - the first which flew over the bar and the second which was saved by Sorensen.
Horsfield was then guilty of his second miss of the game after 69 minutes when he was released by Clement only to push his shot wide of the post when he again just had Sorensen to beat.
Albion also had strong penalty appeals turned down in the 88h minute when Gavin McCann appeared to handle the ball under pressure from Kanu.