The win meant Portugal, who have not missed a major tournament since the 1998 World Cup in France, moved onto 11 points from six matches.
The result also put an end to a five-game winless streak which Portugal had failed to break last Friday when they stumbled to 3-3 draw in Israel.
Ronaldo, watching in the stands because of a suspension picked up in Tel Aviv, saw Azerbaijan's defensive heroics fall apart after forward Rauf Aliyev was sent off for a second yellow card early into the second half.
Portugal took advantage soon after when Bruno Alves, who scored the opener in Israel, sprinted towards a Joao Moutinho corner and towered above the Azeri defence to head in after 63 minutes.
Substitute Hugo Almeida then finished off Azerbaijan with an easy header in the box from a Fabio Coentrao cross with 10 minutes to go.
Russia top the group in the automatic qualification spot with 12 points from four matches.
With Manchester United's Nani also out due to injury, Portugal coach Paulo Bento opted for VfL Wolfsburg's Vieirinha and Zenit St Petersburg's Danny on the wings.
They did not disappoint and created several chances but striker Helder Postiga fluffed his lines in the first half.
"It is a shame that we were so wasteful upfront. We had enough chances to go into halftime winning," Bento told Portuguese television RTP.
The Portuguese kept pressing and centre back Alves, who deputised for Ronaldo as captain, smashed a free kick against the bar.
He finally broke the deadlock when Portugal already had a one-man advantage over an Azerbaijan side without the sturdy defensive ability that coach Berti Vogts used to display for Germany.
"We proved today we have the capacity to qualify. It is in the bad moments that we show our character," Alves said.
It was not all good news for Portugal as centre back Pepe picked up a yellow card and will miss the next qualifier at home to Russia in June.
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