Nuri Sahin's first goals for the club kept Liverpool's grip on the Capital One Cup as Brendan Rodgers' young lions came from behind to win 2-1 at West Brom.
Albion went ahead through Gabriel Tamas but on loan Real Madrid midfielder Sahin levelled before half-time.
Sahin then struck the winner with eight minutes remaining to ensure a Liverpool side that was bearing 11 changes from the side beaten at home by Manchester United on Sunday came out on top.
The home side will be bitterly disappointed at their exit after fielding a strong side but only midfielder Youssouf Mulumbu and striker Romelu Lukaku emerged with much credit.
Albion needed only three minutes to take the lead after a glaring error by Reds goalkeeper Brad Jones. Liam Ridgewell floated a harmless looking free-kick into the Liverpool box from the left flank but Jones, under no pressure, dropped the ball and central defender Tamas kept his volley down as it flew into an unguarded net.
West Brom came close to doubling their lead when Lukaku cut in from the left but his shot was deflected wide by Jamie Carragher. Albion dominated the early exchanges and a fierce drive from Markus Rosenberg forced a low save out of Jones after Lukaku had shaken off the challenge of Carragher.
But Liverpool should have levelled after 11 minutes when debutant Samed Yesil headed wide from Assaidi's centre. Another goalkeeping error, this time by Ben Foster, led to Liverpool equalising after 17 minutes through Sahin, who fired a speculative low 30-yard drive which Foster allowed to slip under his body and into the net.
Liverpool dominated the early exchanges of the second period and Yesil's low shot hit the leg of Foster and somehow bounced up over the bar. Then the former England keeper could only stand and watch as Jordan Henderson's curling attempt from the left of the Albion box struck the bar.
Rosenberg was struggling to make an impact but did force Jones to turn aside an effort from on the edge of the Liverpool area.
Jerome Sinclair became Liverpool's youngest ever player at 16 years and six days when he was introduced as an 81st minute substitute, beating the record of Jack Robinson (16 years and 250 days). Then a minute later Sahin won it for the visitors when he found space at the far post to convert Assaidi's low cross.