The Armenian league leaders had little trouble disposing of their opponents from San Marino, while EB/Streymur claimed a fine 2-2 draw in Andorra
Ismael Fofana scored a hat-trick as Shirak beat Tre Penne 3-0 in the first round of UEFA Champions League qualifying on Tuesday.
The 24-year-old Ivorian was the star of the show as his Armenian side romped to victory against their opponents from San Marino in the first leg of their first-round clash.
The midfielder, who counts England's Charlton and Norway's Fredrikstad among his former clubs, netted the first goal of the 2013-14 UEFA Champions League season with a 36th-minute strike.
The Armenian Premier League table-toppers then gained themselves a significant advantage for the second leg as Fofana netted twice more after the break - firing home again in the 55th minute before wrapping up his hat-trick nine minutes later to give Shirak a comfortable win in Gyumri.
Tuesday's other match saw EB/Streymur of the Faroe Islands come from behind to claim a 2-2 draw at Andorran outfit Lusitans.
Lusitans scored twice in the first 30 minutes, with defender Cristian Martinez netting both goals. His first came via a 24th-minute penalty, before he doubled his account five minutes later.
However, a half-time substitution by EB/Streymur manager Runi Nolsoe paid dividends, as Arnbjorn Hansen struck after 67 minutes, and a Levi Hanssen penalty two minutes later ensured the spoils were shared ahead of next week's return fixture.