The Andorran champions started brightly against their Armenian opponents and took the lead through Marc Pujol in only the fifth minute at the Estadi Comunal d'Andorra la Vella.
Iban Parra provided the delivery that allowed the 31-year-old striker to fire past Artur Toroyan in the Banants goal.
Toroyan was called into action again nine minutes later to deny Juanfer, and slowly the competition debutants began to work their way into the game.
Aram Loretsyan, Gevorg Nranyan and Areg Azatyan all went close for Banants but found goalkeeper Eloy Casals in good form.
Chances were few and far between in the second half with neither keeper forced into a save until the 77th minute when Casals denied Aram Shakhnazaryan.
Santa Coloma were able to withstand late pressure to seal an first-leg victory, although Banants will hope they can turn it round in the return match in Yerevan.
In Tuesday's other match Estonian champions Levadia recorded an impressive 1-0 away win against La Fiorita with a late Heiko Tamm goal.
Neither side was able to break the deadlock during normal time in Serravalle but the hosts from San Marino buckled in injury time at the end of the match.
Midfielder Igor Subbotin combined well with substitute Tamm in the fourth minute and the latter fired beyond Simone Montanari to give Levadia a precious away goal.
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