David Moyes may wonder how Everton emerged from this game unscathed, let alone sporting a two-goal lead, but the manager will have no complaints after his team once again demonstrated their ability to win ugly. Everton will welcome Brann to Goodison Park a week today as the overwhelming favourites to progress to the last 16 of the Uefa Cup, although Moyes will not be underestimating the Norwegian champions, who may feel as aggrieved by the scoreline as the visiting team were flattered.

It took a moment of inspiration from Leon Osman to inch Everton to victory before Victor Anichebe came off the substitutes’ bench to claim the second goal, which could make all the difference in the return leg. The delight and relief on the faces of Everton’s supporters after a record sixth successive win in Europe was understandable, although it did not justify the decision of some of them to run on to the pitch at the final whistle. “We’ve got some momentum at the moment,” Moyes said and few would disagree.

It was not the mismatch the bookmakers had predicted. Everton were odds-on favourites to win, with Brann 6-1, but there was little to separate the teams for most of the night.

With Mikel Arteta and Steven Pienaar injured, Moyes opted to play Tim Cahill through the centre of midfield behind a two-man attack and move Manuel Fernandes out to the right. It gave Everton a disjointed look, although it could still not excuse the poverty of their passing, not least in the first half. “I thought we were happy to keep the ball and go nowhere, but there was a bit more devilment to our play in the second period,” Moyes said.

Brann appeared to be there for the taking in the early stages, with Yakubu Ayegbeni almost making immediate amends for going Awol after the African Cup of Nations when he had a shot saved with only 35 seconds gone, but with Everton conceding possession needlessly, Brann grew in confidence. Even when they fell behind, the hosts would not be deterred and they could easily have drawn level before Anichebe plundered his fourth goal in Europe this season two minutes from time.

Brann’s weakness was that Thorstein Helstad, the striker, could not profit from a series of balls played to him, his control letting him down. Otherwise, Brann might easily have scored the goal their efforts deserved. They did find the net just before half-time, but Eirik Bakke was judged to have fouled Tim Howard as the Everton goalkeeper rose to catch Jan Gunnar Solli’s corner.

Everton were crying out for the invention to match the industry of Phil Jagielka, who was outstanding in central defence, before Osman obliged. The diminutive midfield player had already had a shot tipped aside by Hakon Opdal in the 33rd minute, but the Brann goalkeeper could do nothing about his effort shortly before the hour.

Andrew Johnson got to the byline and crossed, Brann appeared to have cleared the danger, but they did not reckon on Osman, who hit a precise half-volley into the bottom corner from just outside the penalty area. “It was a great strike,” Moyes said.

Everton’s brightest chance before then had come from the otherwise anonymous Cahill, whose blistering 25-yard drive was brilliantly pushed on to a post by Opdal, but Brann had opportunities of their own, not least in the 82nd and 83rd minutes. Njogu Demba-Nyrén had a fine shot tipped aside by Howard before the goalkeeper was called into duty again to save Hassan El-Fakiri’s header on the line.

Everton barely deserved a second, but Anichebe, who has proved an inspired substitute in the Uefa Cup this season, turned home Joleon Lescott’s cross. Moyes’s men march on.

Brann (4-4-2): H Opdal — B Dahl (sub: M Thwaite, 89min), O Bjarnason, K Sigurdsson, E Hanstveit — J Gunnar Solli, H El-Fakiri (sub: E Huseklepp, 75), E Bakke, P Vaagan Moen — T Helstad, A Karadas (sub: N Demba-Nyrén, 69). Substitutes not used: N Udjus, C Guntveit, N Misje, R Winters.

Everton (4-4-1-1): T Howard — P Neville, J Yobo, P Jagielka, J Lescott — M Fernandes (sub: A Hibbert, 89), T Cahill, L Carsley, L Osman — A Johnson (sub: V Anichebe, 76), Yakubu Ayegbeni (sub: L Baines, 90). Substitutes not used: S Wessels, A van der Meyde, J Vaughan, J Rodwell. Booked: Fernandes.

Referee: A Genov (Bulgaria).