Ashley Young and Sidwell were both denied by the Baggies keeper, while Barry also headed wide as Villa tried to reassert their authority.
The visitors replied, with Bednar warming Friedel's gloves with a stinging drive but they seemed to have lost their impetus once Morrison limped off midway through the sesond half.
Instead it was Villa who went closest to extending their lead at the death, with Agbonlahor fizzing a shot across the face of goal.
West Brom thought they might have won a penalty deep into stoppage time when Bednar and then Koren tumbled in the box, but referee Steve Bennett waved away their appeals and awarded a corner.
Aston Villa boss Martin O'Neill:
"Gabriel Agbonlahor played when really a lot of lesser people wouldn't have bothered turning up."
"He has been ill all week, he's only done 10 minutes training and yet he's declared himself fit.
"He did brilliantly and he deserves that goal."
West Brom boss Tony Mowbray:
"We have always been vulnerable to set plays and Scott Carson is disappointed with the second goal.
"In football you need to get people to do their jobs at both ends.
"At one end you need people to score goals and to get rid of it at the other.
"Over the piece we were more than a match for Aston Villa but ultimately we got no points.
"It comes down to quality and our biggest threat was probably a 20-year-old from Arsenal (Jay Simpson).
"We have been looking for that quality in the final third to put teams to the sword."
Aston Villa: Friedel, Reo-Coker, Davies, Laursen, Luke Young, Sidwell (Cuellar 86), Petrov, Barry, Milner, Agbonlahor, Ashley Young.
Subs Not Used: Guzan, Harewood, Delfouneso, Knight, Shorey, Gardner.
Goals: Davies 19, Carson og 41
West Brom: Carson, Hoefkens, Barnett, Olsson, Robinson, Morrison (Morrison 65), Koren, Greening, Borja Valero (Kim 77), Simpson, Moore (Bednar HT).
Subs Not Used: Kiely, Cech, Beattie, Donk.
Goal: Morrison 49
Ref: Steve Bennett (Kent)
BBC Sport Player Rater man of the match: Aston Villa's Ashley Young 7.74 (on 90 minutes).
Please note that you can still give the players marks out of 10 on BBC Sport's Player Rater after the match has finished.
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