Christian Benteke opened the scoring with a superb finish and Gabriel Agbonlahor doubled Villa's lead before half-time. Albion skipper Chris Brunt pulled a goal back early in the second half and then QPR transfer window target Odemwingie equalised seven minutes from time.
Villa dominated the opening 45 minutes, with Charles N'Zogbia in superb form as he produced one of his best performances for the midlands club.
He demonstrated the quality which had helped to keep Wigan in the top flight before his move to Villa during the summer of 2011 and set up the opening two goals.
It was a stunning strike from Benteke that put Villa ahead after 12 minutes. N'Zogbia found Villa's £7million summer signing on the edge of the box and he turned past Claudio Yacob before firing an unstoppable rising shot past Albion keeper Ben Foster for his 10th goal of the campaign.
Villa were posing problems and after 31 minutes Agbonlahor doubled their lead with his fifth goal of the season. N'Zogbia again supplied the telling pass and Agbonlahor wriggled past Gareth McAuley before finding the bottom corner.
Albion began the second half with more purpose and reduced the arrears after 49 minutes.
Substitute Jerome Thomas' low cross was held up and turned back by Romelu Lukaku into the path of the onrushing Brunt, who curled a 15-yard shot past Brad Guzan.
Odemwingie then nicked the ball past Guzan but shot over from a narrow angle. He was not to be denied and after 83 minutes brought Albion level.
McAuley headed a Brunt corner back across goal and Odemwingie reacted first to volley past Guzan on the half turn.
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