A surprise loss to the Republic of Ireland in their last match – during which captain Cristiano Ronaldo was sent off – meant they needed to win on Sunday to be assured of qualification.
They made the ideal start when Renato Veiga headed home early on following a free-kick by Manchester United midfielder Fernandes.
Eduard Spertsyan equalised for Armenia with a close-range finish in the 18th minute, but from then on Portugal took control.
Goncalo Ramos slotted home 10 minutes later before Neves swept in and then got his second of the game from a free-kick.
Portugal scored a fifth on the stroke of half-time when Ruben Dias was fouled inside the box and Fernandes rolled home the penalty.
The scoring continued in the second half as Fernandes fired home with a low strike then converted again from the spot after Carlos Forbs was fouled.
Neves got his third and Portugal’s eighth when he steered the ball home from the middle of the box, before Francisco Conceicao drilled in with seconds remaining to wrap up the big win.
