Defending champions Paris Saint-Germain also advanced out of the playoffs on Wednesday, but Juventus went out after extra-time despite winning on the night.
Fellow Italian club Atalanta completed a remarkable comeback, also at home, with a last-second goal to maintain their involvement in the competition.
Madrid fans held up banners with messages of support for Vinicius - who had scored the only goal in Lisbon a week earlier - before kick-off at the Santiago Bernabeu.
And as the players took to the field, two forceful messages - "No to racism" and "Respect" - were read out.
Vinicius repaid the support with a cool 80th-minute finish, which secured a 2-1 win on the night and 3-1 on aggregate.
"He didn't need to score to send a message or show his mentality," Madrid defender Trent Alexander-Arnold said of Vinicius, who led the line in the absence of injured Frenchman Kylian Mbappe, to TNT Sports.
"He doesn't need to prove anything to anyone because he's shown time and time again how good he is.
"He steps up when we need him the most. He knows his quality and what he brings to the team."
The Brazil star celebrated his goal like he did last week, by dancing beside the corner flag.
"I'm happy that Vini is dancing," Madrid goalkeeper Thibaut Courtois added.
"Because if he's dancing, it means that he is scoring."
Benfica's Rafa Silva netted in the 14th minute to briefly level it at 1-1 on aggregate, only for Aurelien Tchouameni to equalise two minutes later.
PSG, who won the competition for the first time last season, also fell behind to fellow Ligue 1 club Monaco but recovered to draw 2-2 and advance 5-4 on aggregate.
Juventus trailed 5-2 from the first leg in Istanbul, but took the return clash to extra-time thanks to goals from Manuel Locatelli, Federico Gatti and Weston McKennie.
But 10-man Juve were finally brought to their knees in Turin thanks to Victor Osimhen and Barıs Alper Yılmaz strikes for Galatasaray's 7-5 aggregate triumph.
Earlier in the night, Atalanta substitute Lazar Samardzic converted a penalty with the last kick of the game against Borussia Dortmund in the eighth minute of added time following a video review to seal a 4-1 win on the night and a 4-3 victory on aggregate in Bergamo.
With PA & DPA.
