But the win came at a cost as Jurgen Klopp’s side lost influential midfield man Philippe Coutinho and defender Dejan Lovren to hamstring injuries before half-time.
Ibe, who came on for Coutinho proved decisive as he broke the deadlock in the 37th minute, after clever build-up work by Adam Lallana and Joe Allen.
Stoke, bidding to make the final for the first time since 1972, had more possession but struggled to make an impact going forward, with substitute Jonathan Walters wasting a glorious late chance.
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Liverpool are now favourites to meet either Everton or Manchester City in the finals at Wembley.
On a run of just two wins in seven games, Liverpool produced a much-improved performance to head back to Merseyside with a lead ahead of the return fixture on January 26.
The Reds host League leaders Arsenal on Wednesday January 13th, while Mark Hughes Stoke play Norwich City at the Britannia that same day.