That result in Switzerland ensured Hibs progressed 5-3 on aggregate to set up a hugely-anticipated clash against a Villa side captained by former Easter Road star John McGinn, who was part of their 2016 Scottish Cup-winning team.
Youan fired Hibs into an early lead and set up Boyle to level the tie on the night in the 73rd minute, soon after Luzern had got within one goal on the aggregate score. Villa are scheduled to visit Edinburgh for the first leg next Thursday.
Hibs had extended their first-leg lead in stoppage-time at Easter Road last week and they started where they finished as they attacked their hosts.
Boyle was impeded in the penalty box in the act of shooting but was penalised for catching his opponent and Josh Campbell shot straight at the home goalkeeper.
Hibs went three up on aggregate when Youan struck in the 10th minute. The wide player picked up a loose ball on the halfway line following a Luzern throw-in, ran to the edge of the box and hit a shot which hit a defender and looped over the goalkeeper.
Luzern hit back six minutes later after a switch of play put Hibs on the back foot. David Marshall made an excellent stop but the ball was cut back across goal for Jakub Kadak to finish from six yards.
Boyle soon raced clear after a brilliant piece of skill and went down just outside the box after Nicky Beloko grabbed his arm, but the referee played on.
Hibs defended deep after the interval, with Dylan Levitt forced off injured in the 52nd minute after rolling his ankle while charging down a shot.
The home pressure paid off midway through the half when Kemal Ademi got goal-side of Paul Hanlon at a corner to convert a free header from five yards.
But Hibs did not allow their hosts to build any more momentum and killed off the home fans’ hopes in Lucerne when they netted on the counter-attack after the ball was launched forward.
Youan outmuscled defender Marco Burch, who responded by trying to grab the Hibs winger’s shirt. Burch bizarrely stopped looking for a free-kick of his own after getting Yoaun’s arm in his throat but the referee played on and Youan got to the byline.
Boyle had peeled off his marker and swept a left-footed shot under the goalkeeper after meeting Youan’s cutback from six yards out to leave the Hibs fans dreaming of more European adventures to come.
Additional reporting by PA Sport.
