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|Scotland's goalkeeper Craig Gordon saves an attempt from Portugal's striker Bruma during an International friendly football match. (Andy BUCHANAN/AFP)|
Wolves forward Costa opened the scoring late in the first half at Hampden Park.
And despite the absence of Juventus star Cristiano Ronaldo, Fernando Santos's side wrapped up a comfortable victory when Eder and Bruma netted in the second half.
Ronaldo has been left out of the Portugal squad while he fights to clear his name following allegations of rape, which he strongly denies.
Ronaldo wasn't the only high-profile absentee from Portugal's line-up.
Besiktas defender Pepe and Manchester City midfielder Bernardo Silva were allowed to return to their clubs as Santos made a host of changes from the Nations League victory in Poland on Thursday.
Stung by an embarrassing 2-1 Nations League defeat against Israel on Thursday, Scotland were more competitive against quality opposition.
Steven Naismith got one back for Scotland in stoppage-time.
But Alex McLeish's team were left to rue missed chances that could have turned the tide against Portugal.
"I thought it was a good performance. I didn't believe at all that we deserved to be 3-0 down," said McLeish, who has lost six of his eight games.
"We lost stupid goals again. The lads wanted to see the video. We showed them and they owned up to some individual errors.
"Individual errors at this level can be devastating."
Scotland were almost gifted a bizarre early lead when Sergio Oliveira tried to head clear from James Forrest's cross, but instead diverted the ball towards his own goal, forcing keeper Beto to tip it over the bar.
Oliveira helped Portugal threaten at the right end when his through-ball caused panic in the Scotland defence.
Leipzig winger Bruma latched onto the pass but his shot flashed wide from the edge of the area.
Scotland were competing well and Forrest curled in a dangerous cross that Naismith headed just wide.
Eder was teed up by Bruma moments later, but Scotland keeper Craig Gordon was equal to the effort.
The visitors' burst of pressure was rewarded in the 43rd minute.
Kevin Rodrigues whipped in a low cross and Costa held off Andy Robertson's challenge before firing home.
Scott McKenna squandered a golden opportunity to equalise soon after half-time when he dived to head John McGinn's corner wide from close range.
Bruno Fernandes was denied by Gordon, but Lokomotiv Moscow striker Eder killed off the Scots in the 74th minute.
Rising to meet a Renato Sanches free-kick, Eder was unchecked by the Scotland defence as he headed past Gordon.
Bruma put the seal on Portugal's commanding display when he struck in the 84th minute after Jack Hendry carelessly lost possession.
Naismith's curler with virtually the last kick of the contest was little consolation for Scotland.