With Cristiano Ronaldo out with an ankle injury and suspended coach Carlos Queiroz watching from the stands, the Cypriots added to Portugal's woes by stunning them with an early goal.
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In-form winger Ricardo Quaresma impressed in Ronaldo's absence, but the Portuguese midfield failed to gel and their disorganised defence gave the Cypriots several chances to threaten with their simple and fast approach.
But Cyprus responded seven minutes later when substitute Yiannis Okkas beat the a badly timed offside trap to guide the ball coolly into Eduardo's net.
"We knew Cyprus were quick on the break and we wanted depth in defence to counter that and we just didn't have that tonight," said Agostinho Oliveira, who is standing in as interim coach during Queiroz's suspension.
Queiroz's future in the job is in doubt after he was banned for six months for insulting anti-doping agents before the World Cup, but Agostinho said the controversy was not the reason behind the poor performance.
"It's not that. This was a moment of football, it happened today, it could have happened three years ago and it can happen in the future too. The players know to stay away from the controversies and concentrate on the game," he added.
