Home team Liverpool broke the deadlock in the 53rd minute when Villarreal defender Pervis Estupinan scored an own goal at Anfield Stadium.
Reds captain Jordan Henderson crossed the ball from the right flank, but the ball was deflected by Estupinan and misguided the Spanish team's goalkeeper Geronimo Rulli and went inside.
Liverpool made it 2-0 in a quick way.
In the 55th minute, Senegalese star Sadio Mane had a perfect timing to double the score after his Egyptian teammate Mohamed Salah's sharp through ball.
Mane leveled with former Ivorian striker Didier Drogba in the most Champions League knockout goals scored by African players. Both had 14 goals.
Ex-Chelsea and Galatasaray forward Drogba retired in 2018.
In general, Liverpool dictated the tempo of the Villarreal match and suffocated the Spanish team with their football skills.
Liverpool will visit Villarreal in the semifinals' second leg at Estadio de la Ceramica on May 3.
The Reds have an advantage for the 2022 Champions League final in France.
The final will be played at the Stade de France in Paris on May 28.
The winning team of this tie will face Manchester City or Real Madrid in the final.
On Tuesday, Manchester City beat Spanish powerhouse Real Madrid 4-3 in Manchester, England.
The second leg will be held at Madrid's Santiago Bernabeu Stadium on May 4.
