Youngster Dominic Calvert-Lewin came off the bench to grab the goal that handed Everton a 1-0 win away to Slovakia's Ruzomberok on Thursday as they secured their progress to the Europa League play-off round.
Calvert-Lewin, who scored the winner for England in the U-20 World Cup final in June, replaced summer signing Sandro Ramirez in the second half and produced a cool finish with 10 minutes remaining.
That allowed Everton to win the third qualifying round tie 2-0 on aggregate, with progress all that matters for the Premier League side after two performances in which they struggled to convince against the third-placed side in Slovakia last season.
Among the headline winners on Thursday were AC Milan, the seven-time European champion beating Universitatea Craiova 2-0 at San Siro in their second leg to go through 3-0 on aggregate.
Giacomo Bonaventura and teenager Patrick Cutrone scored the host's goals against the Romanian visitor.
Athletic Bilbao, runners-up in 2012, beat Dinamo Bucharest 3-0, with Raul Garcia netting twice, to go through 4-1 on aggregate.
Zenit St Petersburg, Red Star Belgrade, Panathinaikos and Fenerbahce were among the other winners.
Marseille are also into the play-off round after following a 4-2 victory at home to Oostende last week with a 0-0 draw in Belgium in the return.
However, fellow French side Bordeaux were knocked out by the Hungarians of Videoton, the Uefa Cup runners-up of 1985.
Videoton's 1-0 win secured a 2-2 aggregate score as they went through on away goals.
PSV Eindhoven were also knocked out, the Dutch club losing 1-0 away to Osijek of Croatia to go out 2-0 on aggregate.
And Freiburg of the German Bundesliga took a 1-0 lead to Slovenia for their return against Domzale, only to lose 2-0 on the night and go out.
The draw for the play-offs takes place on Friday, with the losing sides from the Champions League third qualifying round also going into the hat.