Molde came out of the blocks in the second half and almost took the lead two minutes after the restart after some neat link up play around the area, and Ferguson had to be alert to hack away the danger.
Larne had their first opportunity moments later when George Marsh blocked a Molde clearance and tried to set up Andy Ryan, but the striker, who scored a hat-trick in the play-off to fire his side to history, rushed his volley and it was well wide.
The hosts looked like a different team from the restart and took the lead when Eikrem fired into the top corner from Eriksen's cut back.
Larne looked to venture forward more after the opener and Sean Graham curled an effort straight at Albert Posiadala from the edge of the area, and the visitors had a huge let off when Brynhildsen blazed a volley over the bar from six yards.
Eikrem was the man making things happen and his powerful drive was tipped over by Ferguson, before Brynhildsen secured the win when he got a lucky bounce of the ball off Want, cut inside and curled an effort into the bottom corner.
Substitute Ihler struck the post for Molde in the closing stages, and Levi Ives had to scramble the ball off the line moments later as the hosts pressed for a third.
McKendry was dismissed in injury time for a wild hack on Amundsen and Ihler capitalised with a close-range finish in the final kick of the game.
Larne will have to reset when they face Dungannon Swifts on Sunday, and their next European fixture is at home to League of Ireland side Shamrock Rovers on 24 October.