The Ligue 1 leaders have had many chances to go ahead, but their finishing has been poor.
PSG have dominated possession and full-back Lucas Digne has been able to get forward frequently.
From the resultant corner, Evian created a rare chance of their own.
Cavani then wasted a glorious opportunity as, unmarked, he headed over from close range.
The overlapping Digne came close moments later, as his low drive across goal skidded just wide.
Ibrahimovic was perhaps fortunate not to be booked just before the half-hour, when his high boot caught the head of Jonathan Mensah.
The Sweden star remained in the action as he crossed to Jeremy Menez, who stooped to head but made a poor contact four yards out.
Menez wasted another chance soon after, volleying over the bar following a perfectly-angled cross from Cavani.