Liverpool set up a semi-final meeting with Chelsea as Raheem Sterling scored twice in a Capital One Cup win away to Championship leaders Bournemouth.
The makeshift striker nodded in the opener after Callum Wilson had missed a glorious chance to put the hosts ahead.
Lazar Markovic's precise finish doubled the lead, but the Reds were thankful for Yann Kermorgant's glaring miss.
Sterling stroked in after the break and, although Dan Gosling bundled in to set nerves on edge, the Reds held on.
The victory should provide a welcome shot of confidence for a Liverpool side that had won only two of their previous 10 games and face an in-form Arsenal in the Premier League on Sunday.