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.
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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 towards the final.
Liverpool, who won the competition in 2019, are attempting to reach their third Champions League final in five years.
"They are a very organised team and we knew they would make it difficult. It was just important that we kept going and believed that we would eventually break them down. We did that with two good goals," Henderson said afterward.
"Majority of the game, our counter-press was really good. It made it difficult for them. But the game is still alive and it will be tough in Villarreal."
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.
"I have to admit, it could have been much worse," Villarreal manager Unai Emery told Movistar Plus.
"We have tried to attack, to pass, to construct but they did not let us do anything and our last resort was to resist defensively in order to survive for the second match.
"We didn't do enough to lament about anything. We have to be humble and try to make the second leg a totally different game. We have to play with more intensity, like we are used to."
The two sides will meet again in the return leg at the Estadio de la Ceramica on May 3.
Information from Reuters was used this this report.