Defeat to Fernando Santos' side follows a woeful reverse against Israel on Thursday and means that McLeish has now lost six of his eight games in charge since taking the top job for the second time in February.

After a largely even opening period, Portugal – which made 10 changes from the side that beat Poland 3-2 on Friday (AEDT) – took the lead in the 43rd minute, Wolves striker Costa turning home Kevin Rodrigues' low cross from close range.

Eder and Bruma struck in the closing 16 minutes to ensure that Steven Naismith's neat strike deep into stoppage time was nothing more than a consolation goal for the host.

After a tepid opening, Scotland almost took a fortuitous lead after 14 minutes. James Forrest's deflected cross caused havoc in the Portugal penalty area and only a smart save from Beto prevented Sergio Oliveria's wayward header from finding his own net.

At the other end, Bruma flashed an effort agonisingly wide of Craig Gordon's left-hand post midway through the first half as the visitors belatedly woke from their slumber.

Portugal's more positive approach was rewarded two minutes before the interval when Costa stole in ahead of Andrew Robertson to prod home from six yards.

Scotland should have pulled level shortly after the restart, but an unmarked Scott McKenna inexplicably headed wide from John McGinn's corner. 

It was made to pay for that miss in the 74th minute when Eder met substitute Renato Sanches' lofted free-kick to head past Gordon.

Bruma added a third six minutes from time, cutting in from the left and firing into Gordon's far post, but Hearts striker Naismith had the final say, curling in after latching onto Gary Mackay-Steven's pass.