The Real Madrid forward first notched with a spectacular left-footed effort, which beat goalkeeper Peter Gulacsi from 20 yards out.
Ronaldo’s second of the night, his 70th career international goal, followed after the half-time interval as he curled a low free-kick from the left flank into the bottom right-hand corner.
The 31-year-old only needed to score once to surpass Robbie Keane’s record of 68. Only Miroslav Klos (71), Sandor Kocsis (75) and Ferenc Puskas (84) have now scored more international goals for a European team.
In the overall standings, Ronaldo’s 70 goals see him sit join-12th, level with former Birmingham City and Coventry City striker Stern John.
The former Trinidad and Tobago frontman reached the same feat during his 16-year-long international career, but did so in 23 fewer games than Ronaldo.
Portugal’s victory saw them move within three points of Group B leaders Switzerland, who beat Fernando Santos’ side in the group’s opening round of fixtures.
After the win, Ronaldo stressed that World Cup qualification matters more to him than any personal record.
“I know how many goals I have but that's not the most important thing,” he told reporters. “What matters is that we won and we're in the fight to go to the World Cup.
“We started out timid. We were slow to react to their tactics, but everything changed with the first goal. The team played better, more confidently, and the goals came naturally.”