The Brazil international's goals in the 27th and 65th minute sandwiched strikes from Marco Asensio and Mohamed Salah to hand Zinedine Zidane's men a sizable advantage heading into the return leg next week.
Madrid went in front just before the half-hour mark when a sprinting Vinicius chested and fired home from a sublime Toni Kroos long ball behind the Liverpool defence.
The goal marked the former Flamengo man's first in the Champions League knockouts. He also became the second-youngest player to score a UCL knockout goal for Real Madrid at 20 years and 268 days, and youngest since Raul in 1996.
Madrid dominated the next exchanges and doubled the lead with help of a ghastly error by Liverpool right-back Trent Alexander-Arnold who, when racing Vinicius to a lobbed through ball down the left, inexplicably played a ball into the path of Asensio with only the keeper to beat.
Asensio's strike -- a chip over Alisson before smashing home into an empty net -- marked the fourth straight match in which the winger has scored in all competitions.
Salah pulled a goal back early in the second half when he slotted home from the middle of the box after a blocked Diogo Jota shot fell to him behind the Madrid defence.
Vinicius restored Real's two-goal cushion in the 65th minute with a guided finish of a Luka Modric rolled cross that went through a defender's legs and off Alisson's hands before squirting in.
While Liverpool pushed, they couldn't find another goal and will now have a steep hill to climb in the April 14 return match at Anfield.
"We didn't let them create anything," Vinicius said after the game.
"The tie isn't over, Liverpool still have a great team and will do everything to win over there so we have to go out on to the pitch just as we did tonight."
Liverpool midfielder Georginio Wijnaldum criticised his side's first-half display and lamented that they switched off for the opening two goals.
"Two moments of not concentrating enough and they scored. We weren't sharp enough," he said.
"We played our own game (in the second half) and that's why we scored. Unfortunately they scored and that makes it more difficult. We hoped for a better result."