Gylfi Sigurdsson took the first step towards repaying his enormous £45m (€49m) transfer fee with a stunning 45-yard strike that helped book Everton a place in the Europa League group stages.
Trailing to Josip Radosevic's wonderful effort just before half-time, Sigurdsson lifted the pressure when he lifted a half-volley past the despairing dive of the goalkeeper in what was his second game for the club.
The home side still kept up the pressure buoyed on by a partisan crowd and earned a penalty following a clumsy Ashley Williams tackle.
However, Said Ahmed Said's weak effort was stopped by goalkeeper Jordan Pickford as Ronald Koeman's men joined fellow Premier League team Arsenal in the draw for the group stages which takes place in Monaco.
Elsewhere, Rosenborg, who knocked Dundalk out of the Champions League before losing out to Celtic, booked their place in the group stages with a 3-2 win over Ajax.
The Norwegians led 1-0 from the first leg and looked to be easing through when Nicklas Bendtner's goal put them 1-0 up at half-time last night.
However, Ajax struck back with two goals in a minute from Amin Younes and Lasse Schoene to put themselves ahead in the tie.
However, Samuel Adegbenro netted with 10 minutes remaining and, as the Dutch side looked for the away goal which would have put them through, Adegbenro netted his second for a 4-2 victory.
The enduring debate over Steven Gerrard's credentials to be included in an all-time Premier League XI was re-ignited as a star-studded BBC selected a line-up that sparked an instant Twitter storm.