The French champions were aiming to equal their longest league run without defeat, which was set in 1994.
PSG had several chances to break the deadlock, but they were let down by the wasteful finishing of their attackers.
The visitors dominated possession and full-back Lucas Digne was able to get forward frequently.
From the resultant corner, Evian created a rare chance of their own.
Cavani then wasted a glorious opportunity at the other end 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.
The sucker punch came on 75 minutes as Nsikulu netted his first league goal of the season following a rapid counter-attack.
Javier Pastore could have levelled the match, but he directed his close-range header straight at goalkeeper Hansen.
Despite waves of pressure from PSG, Evian struck again with three minutes remaining, as Daniel Wass assisted Sougou, who finished crisply from 12 yards.