Howard had little to do against the Norwegian club. His only scare came in stoppage time when a goal was disallowed for a shove on Tim Howard by Eirik Bakke.
Second-half goals by Leon Osman and Victor Anichebe gave Everton a comfortable cushion going into next week's second leg at Goodison Park.
Everton is out of the two English cup competitions but is aiming for a berth in UEFA Champions League qualifying next season. It is currently fourth in the English Premier League.