Liverpool then took the lead four minutes later through the in-form Sturridge, who went round Brad Guzan to finish from a tight angle.
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Seven minutes into the second period Sturridge fizzed across a very dangerous ball, but Ron Vlaar was able to cut it out and concede a corner.
With 15 minutes left, Villa started to up the pressure and Gabriel Agbonlahor had an effort with a half-volleyed snap-shot but sent the ball narrowly wide.
For the second game running the Reds had Mignolet to thank for keeping them ahead, as this time he was equal to a fierce Benteke strike from inside the box.