The signs looked ominous for the former Motherwell boss and his Dons charges when Michael Hubnik opened the scoring for the Czech side after 18 minutes, but Charlie Mulgrew equalised with a majestic free-kick five minutes later.
Lukas Bajer restored Sigma's lead after 63 minutes with an equally magnificent set-piece and Jakub Petr grabbed a third six minutes later.
Substitute Michal Ordos added a fourth in the final 10 minutes with a rasping drive before Tomas Horova rounded off the scoring in the dying stages.
The Dons had an unfamiliar look about them, with Stuart Duff deputising for the injured Zander Diamond in the centre of defence and Derek Young starting the match from right-back.
Reserve goalkeeper Bertrand Bossu was out with a hamstring injury so new signing Stuart Nelson started on the bench.
Sigma defeated Fram Reykjavik 3-1 on aggregate in the previous round and warmed up for the Pittodrie clash with a 2-0 win over Bohemians in their first league game of the season at the weekend.
This was the first taste of competitive action for McGhee's charges this season and their lack of match sharpness was evident in the early stages.
Young's inexperience in his new position was almost costly after 11 minutes when he allowed Hubnik too much space on the left but Tomas Janotka was unable to connect with his low driven cross with the goal gaping.
A minute later the Sigma striker again surged forward but Jamie Langfield and Duff combined to scramble the ball clear.
The inevitable opener for Sigma came when Hubnik reacted quickest to turn the ball home after Langfield had parried Janotka's header from a Rudolf Otepka corner.
The Dons should have equalised a minute later when Sone Aluko crossed for the unmarked Richard Foster but the defender was unable to divert his header goalwards.
But McGhee's men restored parity in spectacular fashion moments later courtesy of a dipping free-kick from dead-ball specialist Mulgrew from 25 yards.
The Czech side continued to enjoy the better possession and the impressive Horova should have done better after 37 minutes but failed to find the target from 22 yards.
The Dons upped the tempo before the break with Nigerian international Aluko darting past two defenders before whipping an inviting ball into the middle that Pavel Dreska managed to head clear with Darren Mackie ready to pounce.
Petr Drobisz, the Sigma goalkeeper, denied Mulgrew a second goal from a set-piece with a fine save seven minutes after the break.
Jakub Petr should have restored Sigma's lead on the hour mark but the striker volleyed the ball over the bar from a near-post Lukas Bajer corner.
The Dons were then dealt a hammer blow when Bajer curled a delicious free-kick into the net from 25 yards for a second away goal.
The free-kick was awarded for a Mark Kerr handball that had looked a harsh decision but there were no complaints about Sigma's third that arrived after 69 minutes when Hubnik released Petr who expertly drilled the ball past Langfield.
As the Aberdeen legs were tiring, Ordos, who was Sigma's top scorer last season, added a fourth with an angled drive that gave Langfield no chance.
Horova rounded off the scoring in the dying stages with a low drive after pouncing on a careless Duff mistake.
The result means the Dons will have to score five times in the Czech Republic next week if they are to progress to the final qualifying round of the Europa League.