After a goalless first half, the visitors gifted Liverpool the opening goal on 53 minutes when Jordan Henderson’s cross was deflected in by Pervis Estupinan.
Liverpool kept the push on, and successfully pounced again just about two minutes after when Mohamed Salah assisted Sadio Mane with the second goal.
The Reds could have gotten more goals against a mostly-defensive Villarreal side, but Thiago hit the post while Fabinho and Andy Robertson had goals disallowed for offside.
The second leg of the tie will be hosted by Villarreal, who would hope to complete a comeback for them to stand a chance of reaching the Champions League final.
Both teams meet again next Tuesday.