FC Pyunik 0-2 PFC CSKA Sofia Bulgarian champions score in each half to establish cushion.
The Bulgarian champions took the lead with their first attack in the 17th minute, as MacDonald Mukasi split the Pyunik defence with a fine slide-rule pass which Todor Yanchev gratefully converted.
Pyunik responded well to falling behind, and Levon Pachajyan went close on 33 minutes when he stole the ball from João Carlos and broke, only to see his shot saved by CSKA custodian Stoian Petrov.
Three minutes after the restart, CSKA doubled their advantage when Emil Gargorov's shot was parried by Pyunik keeper Edel Bete and Mukasi was on hand to score from the rebound.
Late red card
Pachajyan came closest to reducing the deficit on the hour mark with a close-range effort which bounced back off the crossbar, but his team will need to come from two behind in Sofia next Wednesday to progress beyond the second qualifying round. However, CSKA captain Gueorgui Georgiev was sent off in added time and will miss the return.
Home coach Mihai Stoichita said afterwards: "We fought hard enough, but we lacked the experience to match our opponents. Our young players do not have international experience and CSKA are a strong team in Europe. Despite that, we will look for a better result in Bulgaria.
'We outplayed them'
CSKA coach Stoytcho Mladenov praised his players, saying: "I think the result was because of our tactics. Pyunik were not bad, but we outplayed them as a team."