Cavani struck twice as PSG maintained their position at the summit of the pool with one game remaining.
Zlatan Ibrahimovic volleyed home the other goal, his 78th-minute strike coming after Davy Klaassen had cancelled out Cavani's opener.
That result left PSG a point ahead of their final opponents Barcelona, setting up a mouth-watering matchday six clash at Camp Nou.
The French champions, unbeaten in their last 21 outings across all competitions, should enter the clash brimming with confidence, especially having overcome Barca 3-2 at the Parc des Princes.
Cavani said: "We had to win. We must finish first. The [final group match against Barcelona] will be like a final.
"Nothing is easy unless we can replicate the game we produced in the first match."
Head coach Laurent Blanc concurred with his star striker's assessment of their scenario and also praised the team's commitment to pull through in a contest in which they were regularly put under pressure.
He added: "When the group was drawn, the favourite was Barcelona. We will have our destiny in our own hands, but Barcelona will be the favourite as the home side.
"You need to know suffering in a season.
"We are not always in the best form, just like everyone else. It's good to win when you are suffering.
"We do not have all our resources at this time and the statistics were not in our favour - maybe we will become a counter-attacking team!
"To take three points from this great Ajax team was very positive."
