In netting the winner, the Real Madrid forward became the all-time leading goalscorer in European Championship qualification and finals combined, his 23rd strike seeing him overtake Dane Jon Dahl Tomasson and former Turkey striker Hakan Sukur.
It was his 25th goal of the season for club and country, and settled a dour affair which offered little in the way of attacking quality.
Armenia, who defended stubbornly for much of the encounter, remain at the foot of the table with just one point to their name from three matches.
Portugal had much the better of the opening quarter of an hour, but it was Armenia who had the first meaningful effort on goal when Rui Patricio got down low to his right to keep out Henrikh Mkhitaryan's free-kick after the Borussia Dortmund man had been felled by Ricardo Carvalho.
Portugal continued to enjoy the majority of possession after the interval, and Danny went close to an opener when his looping header struck the top of the crossbar before being held by Berezovski under pressure from Ronaldo.
The forward continued to pose a threat, and duly delivered the telling blow 18 minutes from time.
Eder struck the base of the post with a header a minute from time as Portugal went in search of a second, but Ronaldo's goal was enough to secure all three points from what was a laboured performance.
