European football has not often provided Everton with welcome relief in recent years, but after the traumatic events of Saturday’s Merseyside derby, which left David Moyes with a savage sense of injustice, the Everton manager could take comfort from a relatively routine Uefa Cup victory capped by the goalscoring return of Tim Cahill.

The Australia midfield player had been absent since March with a metatarsal injury but took only 14 minutes to justify Moyes’s accurate, if slightly bizarre, description of the 27-year-old as “Mr Johnny-on-the-spot”, setting Everton on course for a win that takes them to within touching distance of qualification for the knockout stage.

Indeed, having seen Leon Osman cap an outstanding move with an excellent finish for his side’s second, Moyes would have been entitled to reflect on an almost flawless night had Joleon Lescott not blundered spectacularly to gift Larissa a 65th-minute goal, triggering an attack of nerves that were settled only by Victor Anichebe’s 85th-minute solo finish.

Moyes’s disenchantment over the weekend’s events was apparent from his programme notes. The Everton manager strongly condemned the reaction of Rafael Benítez, the Liverpool manager, and his players, who offered support to Mark Clattenburg, the referee, whose decision-making had a significant impact on the match. “I have never known such widespread condemnation of a referee for his decisions in one game,” he said. “But some of the comments which came out of the opposition I regarded as a total cop-out. Here at Everton, I always try and give a fair assessment.”

With that out of the manager’s system, Moyes’s players focused admirably on more pressing matters, quickly assuming control against the team who had beaten Blackburn Rovers in the previous round. Cahill’s return immediately brought more fluency to Everton’s forward play, while Mikel Arteta appeared intent on making his 100th appearance for the club memorable. The Spaniard, inevitably, was involved in the build-up to Cahill’s goal, exchanging passes with Osman, whose cross was diverted past Stefanos Kotsolis, the Larissa goalkeeper, by the Australian’s stooping header.

Everton’s dominance appeared total five minutes after the interval when Osman made it two. Cahill moved quickly to halfway before cleverly releasing Leighton Baines, whose first touch found its way towards Osman via Steven Pienaar’s back-heel and the midfield player drove home from 20 yards. The Greek side were given hope when Lescott allowed Cleyton, the Brazil forward, to reduce the deficit.

“We’ve missed Tim,” Moyes said. “He plays in a different way to anyone else in the club.”

Everton (4-4-1-1): T Howard – A Hibbert, J Yobo, J Lescott, L Baines – M Arteta, L Osman, L Carsley, S Pienaar (sub: A Stubbs, 88min) – T Cahill (sub: T Gravesen, 66) – J McFadden (sub: V Anichebe, 66). Substitutes not used: S Wessels, P Jagielka, Nuno Valente, Yakubu Ayegbeni. Booked: Yobo, Lescott, Gravesen.

Larissa (4-4-2): S Kotsolis – M Sarmiento, N Dabizas, I Kyriakidis (sub: A Lampropoulos, 75), S Venetidis – G Gkalitsios, G Fotakis, M Foerster (sub: A Venetis, 78), F Parra (sub: C Kalantzis, 58) – I Bakayoko, C Alexandre Silva. Substitutes not used: F Kipouros, I Kotsios, D Gkikas, P Katsiaros. Booked: Dabizas.

Referee: M Ingvarsson (Sweden).