The Spanish side were resolute in the first half but came unstuck in the second as Henderson’s deflected cross soared over goalkeeper Geronimo Rulli — later ruled a Pervis Estupinan own goal — before Mane poked home shortly after.
Villarreal have enjoyed a remarkable run in the knockout stages of this year’s competition — they stunned giants Juventus and Bayern Munich in the previous two rounds — but Jurgen Klopp’s team were rarely troubled as they dispatched the Spanish side to take a major step toward the final.
Liverpool, who won the competition, in 2019, are attempting to reach their third Champions League final in five years.
Mane enjoyed the best chance in an uneventful first half played mostly in Villarreal’s half. The 30-year-old forward darted into the penalty area as Mohamed Salah delivered a floated cross toward the six-yard box, but Mane could not find the right contact to guide a header towards goal.
Liverpool thought they had broken the deadlock on 50 minutes when Fabinho put the ball in the back of the net, but defender Virgil van Dijk was ruled to be offside when he headed to set up the midfielder.
Klopp’s side remained in control and were dutifully rewarded as Henderson created the breakthrough on 53 minutes. The midfielder struck what looked to be a cross from near the right corner flag, seeing it take a fortunate deflection off Estupinan before looping into the back of the net.
Mane doubled the lead just two minutes later with a prodded finish after Salah rolled the ball into his path inside the box.
Villarreal did not manage a single shot on target as they struggled to make their mark.
The two sides will meet again in the return leg at the Estadio de la Ceramica on May 3.