Arnbjorn Hansen gave the hosts the lead with three minutes gone before namesake Levi doubled the advantage with 38 minutes on the clock.
A Manuel Machado red card on 55 minutes seemed to put the contest beyond his side.
Luis Dos Reis did, however, cut the arrears with 66 minutes gone but Gunnar Zachariasen restored the two-goal advantage six minutes later.
Tre Penne overcame Armenian champions FC Shirak 1-0 courtesy of a Didier Kadio own goal but a 3-0 victory in the first leg was enough to secure progression for Vardan Bichakhchyan’s men.
Champions League Qualifying round one second leg matches
EB/Streymur (Faroe Islands) - FC Lusitans (Andorra) 5-1 (halftime: 2-0) First leg: FC Lusitans - EB/Streymur 2-2. EB/Streymur win 7-3 on aggregate.
Tre Penne (San Marino) - FC Shirak (Armenia) 1-0 (halftime: 1-0) First leg: FC Shirak - Tre Penne 3-0. FC Shirak win 3-1 on aggregate.