Bangladesh suffered a defeat by the same margin in their Russia World Cup qualifier against Tajikistan in Dushanbe in November last year.
Captain Mamunul Islam had said a draw would be enough for them after Lodewijk de Kruif's return as their mentor.
But Thursday's rout sealed their sixth defeat in nine FIFA-approved matches against Tajikistan.
Kruif's men conceded three goals in the first half as Tajik forward Jahongir Ergashev found the back of the net twice in the first 30 minutes.
Parvizjon Umarbaev netted the third five minutes later.
Davronjon Ergashev (49') and Umedzhon Sharipov (75') scored two more in the second half to put one foot into the group phase of the qualifiers.
The second leg will be played at the Bangabandhu National Stadium in Dhaka on Jun 7. Bangladesh drew 1-1 with Tajikistan in the previous home fixture.
In case they fail to avoid the defeat, Bangladesh will get another chance to qualify when they play against Bhutan in the next round of the playoffs in September and October.