PSG had lost three and drawn one of its last four games, and Sunday's game at Parc des Princes was widely considered to be Kombouare's last chance to salvage his job — even though PSG is only three points behind leader Montpellier.
The talk this week had been when, not if, Kombouare will go, with the club's wealthy Qatari backers reportedly pressuring sporting director Leonardo to seek out a bigger name. It was PSG's first win since Leonardo admitted last month that he had met former Chelsea coach Carlo Ancelotti, triggering speculation over a new coach.
"Let's not talk about relief, let's talk about reward for the effort the players put in," Kombouare said. "I've never doubted the quality of the players. It's only the beginning and I'm awaiting confirmation next weekend at Sochaux."
Leonardo did not speak after the game, but Nene made it clear that the players are with Kombouare.
"Of course we're all united," Nene said on Canal Plus television. "We'll try to do our best and we're all with him."
Kombouare says he's determined to stay.
"They've shown that they want to carry on with me," Kombouare said. "I am very proud to be PSG coach and I want to stay as long as possible. I was here before, I'm part of the project (now) and I still want to be in the future."
All the goals came in a frantic second half. After Kenya striker Dennis Oliech cancelled out Christophe Jallet's opening goal, Nene set up Menez in the 76th minute and scored a penalty five minutes later.
After 16 matches, Montpellier has 36 points, while PSG has 33 and third-place Lille has 31.
"A season is very long, it's a marathon, and you're always going to have difficult times," Kombouare said. "I would rather it happens now than in March or April, when it could be even more damaging.
"Maybe we rested on our laurels a bit. We were walking on water at the start of the season and that gave us the impression nothing could happen to us."In Sunday's other match, Bordeaux beat Nancy 2-0.
With the crowd fearing another letdown, Nene found space on the left and his cross to the back post fell perfectly for Menez to beat goalkeeper Olivier Sorin.
Nene looked to have put the game beyond Auxerre when he was fouled by centre half Stephane Grichting and sent Sorin the wrong way from the spot.
But PSG had to sweat for its victory as Oliech's pace drew defender Zoumana Camara into a clumsy foul, and Dariusz Dudka smashed the penalty into the top corner in the 87th.
Kombouare recalled Menez and record signing Javier Pastore after they sat out Thursday's 2-0 loss to Salzburg in the Europa League.
PSG only carved out two half-chances in the last 10 minutes of a drab first half.
Pastore tried to dribble his way through the Auxerre defence but lost the ball before he could shoot.
Kevin Gameiro, looking for his first goal since Oct. 16, threw himself at Jallet's cross but could not quite connect.
Auxerre went closest to taking the lead when midfielder Alain Traore's long shot forced goalkeeper Salvatore Sirigu into action with a smart save.
Jallet's goal was the product of some good teamwork and finally broke the stalemate in the 52nd.
Brazilian winger Nene crossed and Gameiro nodded the ball down to Menez, who decided against shooting and passed the ball into the path of Jallet to finish the move with a clinical finish.
But nerves again got the better of PSG's players and Oliech equalized all too easily in the 59th.
The Kenya striker skipped past PSG leftback Siaka Tiene before cutting inside the penalty area and beating Sirigu at the second attempt after the Italian 'keeper kept out his first effort.
Nene then went close with a chip that drifted just over, before Anthony Le Tallec almost put Auxerre ahead in the 69th. He profited from a mix-up in defence between Mamadou Sakho and Camara, but shot just over.
At Bordeaux, the home side took the lead in the first minute.
Nicolas Maurice-Belay's whipped cross from the left fell to David Bellion and his shot was turned onto the post by goalkeeper Guy N'dy Assembe. But Plasil followed up and buried the rebound.
Bordeaux doubled its lead when Brazilian defender Henrique headed in Plasil's corner in the 51st.
In Sunday's later match, Lyon hosted Toulouse in the battle for fourth place.