PSG won by 4-0, with Ibrahimovic putting the title-challengers in front on 28 minutes before Ezequiel Lavezzi – who scored the winner in PSG’s midweek Champions League win over Porto – was again on target moments later.
Thiago Motta and Kevin Gameiro added late strikes as the French capital club secured just a second league victory in six attempts.
“We played a good match. It was a good performance from the team, with good play, a good attitude and an attacking style. Everything went well today,” said Ancelotti.
“After the defeat at Nice [last Sunday], we have played two good matches. Next week, we have two more difficult games, against Valenciennes and Lyon. With this attitude things will be better,” he added.
The result moved the Parisians up to second on 29 points, level with arch-rivals Marseille.
Bertrand Laquait had to be alert to keep out an early header from Ibrahimovic at Parc des Princes, but there was nothing the Evian goalkeeper could do as the home side went in front on 28 minutes.
Neat interplay between Christophe Jallet and Javier Pastore on the right flank led to the latter crossing for Ibrahimovic, who poked the ball past Laquait from close range to give PSG the lead.
The Swede then displayed great strength three minutes later, chesting down Jeremy Menez’s lofted pass into the path of Lavezzi, who turned past a defender before curling low into the far corner via the inside of the post.
Lavezzi was denied a second goal of the afternoon as Laquait clawed away the Argentine’s header, but the hosts asserted their dominance in the second period.
Ibrahimovic was only prevented from adding to his account by the frame of the goal as his prodded effort looped over Laquait but rebounded off the left upright.
A 25-yard strike from Olivier Sorlin represented a rare opportunity for Evian, while substitute Saber Khelifa struck tamely at home goalkeeper Salvatore Sirigu when well-placed.
Motta, who was making his return after a month on the sidelines, further increased PSG’s advantage, notching his first goal of the campaign as he swept home Pastore’s low cross on 84 minutes.
Gameiro then added a fourth two minutes later – moments after coming on to replace Motta – capping off a fine move after Menez had unselfishly squared for the France striker after he was put through by Ibrahimovic.