Ronaldo's goals extended his record as the highest scorer in men's international football to 140 and underlined his enduring motivation to keep setting more benchmarks before his storied career comes to an end.
The 40-year-old recently signed a new contract with Saudi Arabian club Al Nassr and led Portugal to victory at the UEFA Nations League last summer.
The World Cup is the one major trophy that still eludes him - leaving him behind Lionel Messi, who lifted soccer's biggest prize with Argentina in 2022.
Next year would likely be Ronaldo's last chance to win it when the tournament is staged in the US, Canada and Mexico. Like him, Messi could also be playing at a sixth World Cup, setting the pair apart from any other player, with a host of names having appeared in five.
Ronaldo struck in each half at the Vazgen Sargsyan Republican Stadium on Saturday as Portugal made a flying start in Group F.
His second saw him roll back the years with a thunderous shot from around 25 metres. He wheeled away in celebration with his arms outstretched.
Joao Felix also scored twice and hit the opening goal after just 10 minutes, while Joao Cancelo was also on target.
"It was a near-perfect performance," said Portugal midfielder Vitinha.
England maintained their 100 per cent qualifying record with a 2-0 win in a dull affair against Andorra at Villa Park.
Thomas Tuchel's team are top of Group K with four straight wins after an own goal from Christian Garcia and a Declan Rice header.
Harry Kane was left frustrated as England failed to convince again under Tuchel.
A 1-0 win against Andorra in June was described by one British newspaper as England's "worst ever." It was followed by a 3-1 home loss against Senegal in a friendly before the end of the season.
Tuchel made 10 changes to his squad and while there was an improvement, England still had to toil against the 174th-ranked Andorrans.
"The energy was right, quality was there. We should have scored more," Tuchel said.
England's all-time leading scorer Kane could not extend his record, with his best chance coming when failing to connect with James's first-half cross with an open net to aim at.
Also in Group K, Serbia beat Latvia 1-0 to move up to second in the table. England play Serbia on Tuesday in what is likely to be their biggest test in the group.
In Group F, Ireland fought back from two goals down to secure a 2-2 draw against Hungary.
Bosnia and Herzegovina and Austria maintained their perfect records in Group H.
Veteran striker Edin Dzeko scored twice as Bosnia routed 10-man San Marino 6-0 to top the group on 12 points after four games.
Austria have played a game less and are second after Marcel Sabitzer's penalty sealed a 1-0 win against Cyprus.
