Ian Baraclough’s side conceded the only goal of the game four minutes before half-time when Daniel Chima Chukwu drilled the ball low into Gary Rogers’ net after a mazy run.
Chima Chukwu and Joinge Berget were a constant threat to the Rovers defence in which Jeff Henderson, Gavin Peers And Iarflaith Davoren played superbly, particularly in the opening half.
Sligo held their own for half an hour but Molde began to expose weaknesses across the back as the half came to a close.
Lee Lynch had a top drawer game for Sligo with his runs down the wing keeping Molde at full stretch.
David McMillan had an opportunity for Rovers in the 23rd minute but the visitors somehow managed to clear their lines. Molde continued to dictate the play at the start of the second half but Rovers gradually began to play with more conviction as the half progressed.
Iarflaith Davorens’ clever ball from the halfway line in the 56th minute caused some anxious moments for the Norwegian champions but again there was no Sligo player positioned to make the move count.
Sligo peppered the Molde goal during the closing stages as the 3,840 crowd cheered on the Bit O’Red, hoping that the equalising goal would arrive.
Joseph Ndo went close for the Reds with a sizzling shot in the 67th minute but the ball missed the target by inches and Sligo now face a daunting trip to Norway.
* The legendary Dixie Dean, who played for Sligo Rovers in 1939, was remembered when three generations of the striker’s family, including his daughter Barbara, were introduced to the crowd at half time.
SLIGO ROVERS: Rogers, Davoren, Peers, E McMillan, Henderson, Elding, Gaynor, Lynch, D McMillan, Ndo, Connelly.
Subs: Djilali for D McMillan 59 mins, Keane for Henderson 71 mins, Martin for Davoren 77mins.
MOLDE FC: Hyland, Lamnes, Toivio, Forren, Simonsen, Mostrom, Ekpo, Berghestat, Berget, Coly, Chima Chukwu.
Subs: Moraes for Coly 17mins, Tripic for Mostrom 76mins, Hovland for Berget 83mins
Referee: Evander Bovlaoi, Belgium.