Already 5-1 up from the first leg of the third qualifying round tie, the Czech side showed no mercy as they romped to victory at the Andruv Stadium.
All the goals came before half-time, with Tomas Janotka, a Marek Kascak penalty and Michal Hubnik - his second of the tie - all finding the net.
It could have been worse but for outstanding Dons goalkeeper Jamie Langfield, who also saved from the spot.
Otherwise, it was another inept defensive performance, compounding the misery of the travelling supporters following reports of skirmishes involving rival fans in Olomouc.
New Aberdeen boss Mark McGhee gave all but one of the team who started the first leg a chance to redeem themselves.
The only change saw striker Chris Maguire come in for Derek Young, which meant Darren Mackie dropping back into midfield.
Despite their mammoth lead, Sigma also made one alteration, Kascak replacing Rudolf Otepka at the back.
Any thoughts the visitors had of salvaging some pride were ended inside a quarter of an hour as their opponents picked up where they left off at Pittodrie.
It took less than six minutes for Janotka to fire Sigma ahead from the rebound after Tomas Horava's effort had hit the post.
It was 2-0 eight minutes later after Mark Kerr brought down the goalscorer inside the penalty box and Kascak sent Langfield the wrong way from the spot.
In between the goals, Maguire twice went close, seeing his first effort parried by Petr Drobisz and his second drift wide.
Sigma showed no sign of easing up, with both Ladislav Onofrej and Horava letting fly from range but too close to Langfield.
Sone Aluko followed suit at the other end midway through the half before Lee Miller nodded a Charlie Mulgrew corner over the bar.
With half-time approaching, Langfield held onto a Hubnik header and a shot from Horava.
But he was beaten for the eighth time in the tie in stoppage-time as Hubnik escaped the attentions of Mulgrew and slotted the ball home.
The pummelling looked set to continue three minutes into the second half after Langfield felled Jakub Petr in the area.
But the goalkeeper - named in the Scotland squad this week - made amends with a fine save from Michal Ordos, who had come on for the excellent Horava during the interval.
Langfield picked up a yellow card for the foul but was at his best again to beat away another Ordos effort.
The keeper also grasped a long-range shot from Petr, who was withdrawn for Pavel Sultes shortly before the hour mark.
The substitute almost immediately forced another outstanding stop from Langfield and Aluko blazed over from distance at the other end.
Sigma's final change saw Otepka replace Hubnik, while Sultes twice went close to a fourth goal on the night before Richard Foster was booked for fouling the forward.
With time running out, Daniel Rossi, Janotka and Sultes were all off target.
Aberdeen brought on Mitchell Megginson for Maguire, while Otepka and Sultes both tested Langfield again before the final whistle put the visitors out of their misery.