Gabriel Agbonlahor put Aston Villa in front after 11 minutes at Anfield and the second-placed visitors clung on to preserve their unbeaten start to the season.
There was no sign of Villa's young team buckling under the pressure and after 81 minutes Weimann drove over a low cross which was turned in by Benteke to spark wild celebrations from the home players and fans.
West Brom, meanwhile, have ended a run of three consecutive defeats, and the point secured by Odemwingie's goal was enough to take them level on points with both Arsenal and Liverpool in the Premier League.
Gaby Agbonlahor scored in the 29th minute and then left with an injury in the second half as Aston Villa beat the Chicago Fire 1-0 in a friendly on Saturday.
Spain coach Vicente del Bosque insists England don't deserve to be written off as Euro 2012 also-rans because they remain a leading force on the international scene.
Aston Villa striker Gabriel Agbonlahor on Friday withdrew from the England squad to face Spain and Sweden after sustaining a slight hamstring injury, officials confirmed.
Manchester City proved there is no hangover from the Carlos Tevez controversy as a 4-1 victory over Aston Villa at Eastlands lifted them to the top of the Premier League on Saturday.
Striker Gabriel Agbonlahor helped give Aston Villa its first ever home Premier League win over Wigan on Saturday, scoring one goal and setting up the other in a 2-0 victory.
QPR snatched a dramatic 1-1 draw against Aston Villa as Richard Dunne scored an own goal in stoppage time at Loftus Road on Sunday.
Aston Villa and Wolverhampton Wanderers are unbeaten in the Premier League after the local rivals drew 0-0 on Saturday.