Lacklustre St Johnstone wilted in Yerevan as Mihran Manasyan's second-half strike gave Alashkert a deserved victory on their European debut.
Alan Mannus denied the Armenian side with two fine saves before Manasyan gave them a 60th-minute lead in this Europa League first-leg qualifier.
Tommy Wright's team tried to retaliate but failed to threaten.
The Perth side must improve in the second leg at home at McDiarmid Park to reach the second qualifying round.
And should the team who finished fourth in the Scottish Premiership make it into the next round, they would face either Red Star Belgrade of Serbia or Kairat Almaty of Kazakhstan.
Abraham Khashmanyan's Alashkert side started brightly and, after they forced a corner in the opening minute, Saints' Murray Davidson suffered a nasty head wound as he helped clear the visiting lines.
With the midfielder off the field receiving treatment for six minutes, the Perth side were on the back foot and Mannus was called into early action to save shots from Gevorg Karapetyan and Siarhei Usenia as the home side dominated possession.
Saints eventually got their first shot on goal after half an hour against the team that finished fourth in the Armenian top flight.
Good link-up play on the edge of the box between new signing John Sutton and David Wotherspoon led to the latter's shot being pushed around the post by Gevorg Kasparov in the home goal.
After water breaks in the searing heat, Mannus dived low to his left to tip away a shot from Narek Gyozalyan from 25 yards.
Davidson, still suffering from the earlier head knock, was replaced with Scott Brown just before half time and Saints suffered a further blow when Alashkert made their dominance tell with what was to prove the winning goal.
Winger Karen Muradyan cut the ball back from the by-line and Manasyan hammered the ball high into the roof of the net past a despairing Mannus.
Saints tried to respond and Sutton headed over from eight yards under pressure, but Wright's side rarely threatened the home goal.
A cooling breeze began to blow through the stadium as dusk fell, but this was little help to Saints as they struggled to cope with the intense heat.
With only two minutes left, Chris Kane, who had replaced Sutton, found space on the edge of the six yard box, but the substitute striker's effort was weak and Saints will now have to rely on winning next week's second leg in Perth.
- 19MinasyanBooked at 80mins
- 17UsenyaSubstituted forManasyanat 59'minutes
- 21GrigoryanSubstituted forHovsepyanat 90+5'minutes
- 22GyozalyanSubstituted forAraujo dos Santosat 80'minutes
- 3Araujo dos Santos
- 15McKayBooked at 45mins
- 8DavidsonSubstituted forBrownat 45'minutes
- 11SuttonSubstituted forKaneat 70'minutes
- Jakob Kehlet