Ronaldo equalised with a penalty just before the half-hour mark, added a second 10 minutes after the break and struck a superb third in the 58th before Tiago Mendes was sent off.
Portugal now lead Group I with 12 points from five games ahead of Denmark, who have seven from four, along with Albania, before hosting second-bottom Serbia later on Saturday.
Armenia coach Sargis Hovsepyan was in charge of his first match for the hosts who looked comfortable early on and took the lead in the 14th minute through forward Marcos Pizzelli whose free-kick flew into the top corner via the underside of the bar.
The visitors levelled through Ronaldo's spot kick after Henrikh Mkhitaryan fouled playmaker Joao Moutinho.
Ronaldo then put Portugal in front when he capitalised on a mix-up between Robert Arzumanyan and goalkeeper Roman Berezovski to score into an empty net.
Three minutes later, the Real Madrid forward completed his treble with a stunning 20-metre strike into the top corner.
Portugal midfielder Tiago was sent off for a second bookable offence just past the hour mark leaving the visitors to sit back and defend in the closing stages.
Armenia's Hrayr Mkoyan reduced the deficit with his first goal for his country after a mistake by keeper Rui Patricio but Portugal held on despite coming under late pressure.
Basement side Armenia are level on one point with the Serbs.
(Reporting by Dmitriy Rogovitskiy; Editing by Ken Ferris)
