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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Winger Efstathios Aloneftis combined well with Michalis Konstantinou to find space at the edge of the box and produce a fine lob over Eduardo in the third minute.
Hugo Almeida levelled on eight minutes with a flying header after latching on to a Nani cross, but Portugal were behind again three minutes later when a poor back pass by Raul Meireles allowed Konstantinou to score easily.
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.
Meireles made up for his earlier error by scoring from a long-distance effort in the 29th minute, and Portugal created several chances before Danny headed in five minutes after half-time.
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.
Midfielder Manuel Fernandes took advantage of a loose ball to fire in from distance on 60 minutes, but Avraam exposed a poor concentration and marking in the Portuguese back line again with a headed goal on 88 minutes.
"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.
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