Scotland's choice of opponents had caused controversy in the run-up to the fixture, with elements of the local media labelling it an "embarrassment" to the Scottish Football Association in the wake of the FBI's corruption investigation into the award of the 2022 tournament.
There had also been widespread calls among Scotland supporters to boycott the match because of human rights concerns.
Many fans, however, still made the trip to Edinburgh's Easter Road stadium, passing a gathering of Amnesty members and supporters on their way in.
The organisation's Acting Programme Director for Scotland Pauline Kelly told Reuters it was not intended to be a protest.
They were "there in solidarity" with the migrant workers in Qatar who Amnesty say are suffering "horrific human rights abuses" building the infrastructure for the 2022 tournament that is now fighting controversy on a number of fronts.
A recent Amnesty report said Qatar was doing little to improve conditions for its 1.5 million migrant workers despite promising reforms last year.
Qatar's arrival in Scotland came after the FBI confirmed this week that their investigation into corruption at socccer's world governing body FIFA was now scrutinising the award of the 2018 and 2022 tournaments.
Amnesty restricted their action to outside the stadium and inside it was a tame affair on and off the pitch.
Unlike Qatar's friendly with Northern Ireland in Crewe on Sunday, where the home fans chanted about bribery and waved bank notes towards the pitch, the Scottish supporters were in more of a party mood.
The visitors' national anthem was respectfully observed, there were no audibly hostile chants or unsavoury banners and a drab win for the hosts was enlivened more by a first-half streaker than by Matt Ritchie's 41st-minute winner.
Scotland striker Steven Naismith succinctly summed up the match: "Overall it wasn't the greatest result," he said.
There was a trophy up for grabs, with purple ribbons adorning the Qatari Airlines Cup, but this was little more than a glorified training exercise for the Scots who play Ireland away in a crucial Euro 2016 qualifier next Saturday.
Scotland are third in Group D on 10 points, one place and two points above Ireland, behind leaders Poland (11) and second-placed Germany (10). The top two teams qualify automatically for the finals along with the best third-placed team.
(Writing by Toby Davis in London; editing by Ken Ferris)
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