Gianni De Biasi's men started the game as heavy underdogs against a side widely expected to dominate Group I, but they left Aveiro with all three points as Balaj stole the show on a memorable night for the visitors.
Portugal were without talisman Cristiano Ronaldo after head coach Paulo Bento deemed him not physically up to being included in the squad.
And in the absence of the Real Madrid forward they struggled for invention and guile, as their campaign got off to a disastrous start.
Bento has been tasked with restoring Portugal's standing following their disappointing group-stage exit at the World Cup, and they were well in control of the first half - Nani wasting arguably their best chance when he shot wide when free in the area.
But Albania also carried a threat and after racing out of the blocks brightly after the restart, they were rewarded in the 52nd minute when Balaj thumped Odise Roshi's delivery past Rui Patricio for the winner.
Bento's men turned the screw in search of an equaliser and substitute Ricardo Horta hit the woodwork late on, but there was no way through.
Unsurprisingly, Portugal started on the front foot and Nani fired an early warning when he linked well with Joao Moutinho to find space on the right of the area, only to shoot past the far post.
Albania then had Amir Abrashi booked for tugging down Nani in the 22nd minute and from the resulting free-kick, the unmarked Vieirinha met Moutinho's delivery but he glanced his header straight at Etrit Berisha.
A lull in proceedings followed as Portugal dictated possession - although they struggled for fluency against a series of robust Albanian challenges.
Portugal finished the half strongly, though with Mergim Mavraj deflecting Nani's 20-yard goalbound shot wide, before Pepe headed over at the back post after Vieirinha had flicked on Nani's free-kick.
Having scarcely threatened in the first half, Albania gave Portugal a scare shortly after the restart when Roshi escaped the attentions of Fabio Coentrao and his ball across the six-yard area narrowly missed the outstretched foot of Balaj.
However, Portugal did not escape twice as the same combination handed Albania a shock lead in fine fashion.
Roshi evaded the attentions of Ricardo Costa thanks to some neat footwork before crossing into the area, where Balaj showed superb athleticism to lean back and smash a first-time volley past a despairing Rui Patricio.
Stunned into action, Portugal upped the pressure and Coentrao dragged a shot narrowly wide shortly after the hour mark when he found space at the back post.
The hosts then went even closer as substitute Horta crashed a 20-yard strike against the crossbar and Pepe blazed the rebound over the from eight yards.
Nani wasted a great chance when he met Coentrao's centre but headed wide from the middle of the box, before Andre Gomes forced Berisha into a fingertip save in the closing stages.
Bento must now pick his side up ahead of next month's friendly with France before they prepare for their next qualifier in Denmark.
Meanwhile, Albania - whose next Group I contest is also against the Danes - can revel in one of the greatest triumphs in their history.
