Sekou Sanogo had initially given the visitors the lead but Lukaku struck twice in five minutes to put the tie to bed. Kevin Mirallas made it 3-1 on the night just a few minutes before half time.
Everton had done themselves a lot of favours going in to this second leg after winning 4-1 away in the first leg.
The Toffees made a slow start, giving the visitors a slight glimmer of hope, especially as they managed to go ahead just 13 minutes in, Tim Howard save Milan Vilotic’s initial header before Sanogo reacted to put in the rebound.
Youngs Boys almost doubled their lead just moments later as Scott Sutter headed against the woodwork from a corner.
However, Everton did soon find their feet in the game, and managed to get themselves back on level terms when ‘keeper Marco Wolfli fouled Naismith in the area and the referee pointed to the spot.
Lukaku put the penalty away with no problem and no more than five minutes later he doubled his tally for the night and put Everton ahead, the striker volleyed the ball home after Luke Garbutt picked him out with a long ball.
Everton were now well in control of the tie, and it could have been more, Barry, Alcaraz and Kevin Mirallas all missing good chances.
The returning Darren Gibson, making his first start for three months set up Everton’s third goal of the night, his pass found Mirallas who side-footed home.
The hat-trick chasing Lukaku was substituted minutes after the break, seeming to be holding his hamstring at the time but his manager later suggested that the switch was simply down to tiredness.
Everton were strolling to their first home win of the year, Mirallas unfortunate not to have got himself another goal, and Kone saw his effort deflect off the post.
Everton through to the next round and find themselves being the only British team left in the tournament.
By Connor Billington
