Everton and AC Milan secure Uefa Europa League progress to play-off round
Zenit St Petersburg, Red Star Belgrade, Panathinaikos and Fenerbahce and
Marseille are also into the next round
Calvert-Lewin, who scored the winner for England in the under-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 champions 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 hosts’ goals against the Romanian visitors.
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.
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.