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The visitors defended deep and in numbers, but Henrikh Mkhitaryan led a 14th-minute counter-attack with a driving run that was halted by a despairing Ricardo Carvalho challenge which earned the veteran defender a yellow card.
From the resulting free kick, the Borussia Dortmund midfielder saw his deflected shot parried away by Rui Patricio.
Mkhitaryan continued to pose a threat with his pace and saw a cross spin into the side-netting after taking a big deflection off Raphael Guerreiro, before Danny sent a tame effort into the arms of Roman Berezovsky at the other end.
Cristiano Ronaldo was relatively subdued in the opening quarter of the game, but it was only a matter of time before he came to life.
The 2013 Ballon d'Or winner fired a shot straight at Berezovsky before seeing his subsequent effort deflected narrowly over the bar.
Albania were content to soak up the pressure before pouring forward in numbers, and Mkhitaryan teed up Kamo Hovhannisyan for the game's best chance with a cleverly disguised through-ball, but the 22-year-old struck the ball at an advancing Patricio when one on one.
There was controversy shortly before the break as Pepe was shown a yellow card for tugging back his opponent, but replays seemed to show the Real Madrid defender stamping on the Armenian winger's chest too.