Everton grabbed two second-half goals to put one foot into the last 16 of the UEFA Cup against Brann Bergen.
Tonight’s first-leg triumph was clinched thanks to strikes from Leon Osman and substitute Victor Anichebe.
Everton had slowly taken control of the match and eventually made themselves odds on the complete the job in next Thursday’s second leg at Goodison Park.
Everton started with a 4-4-2 formation with Andy Johnson alongside Yakubu up front, which showed their intent to attack even if it is not David Moyes' favourite formation.
But it was the hosts who almost went ahead in the eighth minute when Jan Gunnar Solli’s free-kick curled into the box and Karadas’ instinctive header flashed over the bar.
Everton seemed content to soak up Brann’s pressure and created precious little in the opening stages, while Bakke was pulling the strings in midfield.
The visitors’ first chance came when Leon Osman saw a 12-yard effort saved by Hakon Opdal, the Norwegian goalkeeper who was on the wrong end of a 3-0 defeat by Wales in Wrexham last week.
Brann continually got into the heart of Everton’s area, but their efforts were smothered, with some difficulty.
Johnson set up Osman on 33 minutes for a snapshot which was turned away by Opdal, but this was not an assertive Everton performance.
Lee Carsley fired over from the edge of the box, but it did not ignite a match that lacked drive and direction.
On the stroke of half-time Tim Howard fumbled a Solli corner over the line, under pressure from Karadas, and referee Anton Genov ruled the effort out.
There was clearly a need for Everton to be more positive after the break, and Tim Cahill responded with a 25-yard effort which cracked against Opdal's left-hand post in the 52nd minute.
And just before the hour mark the took the lead.
Cahill won possession and the ball was played into Andrew Johnson, who turned Kristjan Sigurdsson in the box before drilling in a low cross.
The ball was only half cleared to the edge of the box and Osman capitalised by cracking a low drive into the far bottom corner.
Brann responded by sending on newly signed striker Njogu Demba-Nyren for his debut in place of Karadas, while Manuel Fernandes was booked for a 69th-minute foul on Bjorn Dahl.
Everton pressed for a killer goal and Fernandes forced Opdal into a fumbling save at the foot of a post before Victor Anichebe came on for Johnson in the 75th minute, with the Norwegians sending on Erik Huseklepp for Hassan El Fakiri.
Howard was forced into a plunging save to keep out a Demba-Nyren long range drive before Thorstein Helstad forced a scrambled save from Howard.
But Everton got the crucial second goal two minutes from time when Fernandes sent Joleon Lescott down the left to supply a perfect cross for Anichebe to guide into the net, his fourth goal in this increasingly-impressive European run.
Tony Hibbert came on for Fernandes and Michael Thwaites replaced Dahl for the Norwegians, but the victory was secured by then.