Fernando Santos's side suffered a 2-0 defeat to Switzerland in their Group B opener last month, but responded in style as four Ronaldo strikes and goals from Joao Cancelo and Andre Silva secured all the points against a side that finished two players short during a match that was marred by ill discipline.
It took less than two minutes for the home side to make the breakthrough, with Ronaldo volleying home from inside the box after Andorra failed to clear a second corner in quick succession.
Less than two minutes later, Portugal, who were full of purpose after the Switzerland defeat, had their second when Ronaldo headed a Ricardo Quaresma cross into the bottom corner as the visitors simply folded under the pressure in the early exchanges.
Andorra actually had a half-chance of their own in the 12th minute when Victor Rodrigues struck one from outside the Portugal box, but the 18-year-old's effort was always moving wide of the post.
Ronaldo should have had his hat-trick in the 20th minute when Cancelo danced past a couple of challenges before delivering a cross onto the head of Ronaldo, but the Real Madrid forward headed away from Josep Gomes's goal.
Portugal had another chance in the 28th minute when Quaresma delivered a free kick onto the head of Jose Fonte, but Andorra goalkeeper Gomes was on hand to make a point-blank save to keep the score at 2-0.
The opportunities continued to arrive for the home side as Andre Gomes and Ronaldo came close to a third in the latter stages of the first period, before Andre Silva rattled the crossbar with a close-range header in the 36th minute.
The pressure was relentless though and Portugal eventually had their third in the penultimate minute of the first period when right-back Cancelo somehow squeezed the ball past Gomes from what seemed an impossible angle after breaking into the Andorran box.
Less than two minutes into the second period, Portugal had their fourth and Ronaldo completed his hat-trick as the 31-year-old found the bottom corner with a volley after meeting a cross from Gomes.
Joao Moutinho and Andre Silva both had opportunities to add to the scoring before the hour, but Andorra goalkeeper Gomes made two smart saves in quick succession to keep the score down to 4-0 with 30 minutes of football to play.
Andorra were reduced to 10 men in the 62nd minute, however, when Jordi Rubio, who was an accident waiting to happen all night, picked up his second yellow card for a terrible challenge on Ronaldo. Ronaldo bounced straight back, however, and scored his fourth of the night in the 68th minute when he fired home from close range after Fonte had won a header at the far post.
It got worse for the visitors in the 71st minute when Marc Rebes was sent off for a lunge on Ronaldo and Portugal were absolutely rampant as they went in search of more goals. Andre Silva should have scored with a close-range header 13 minutes from time, but Gomes made a stunning save.
Portugal did have their sixth in the 86th minute when Andre Silva converted from close range, however, and that was how it finished in Aveiro as the home side collected all the points in extremely comfortable fashion.
Next up for Santos's side is a trip to Faroe Islands on Monday, while Andorra's search for just their second ever competitive win will continue at home to Switzerland on the same night.