"This series is very important for Team India. We have gained the momentum in the series and want to keep it going," Zaheer, who took a haul of eight wickets in the match, told reporters after the match.The second and final Test starts in Bangalore on October 9.
Zaheer credited senior batsman VVS Laxman, who hit an unbeaten 73, for the win.
"We call him Very Very Special (VVS). He has done it so many times for India. He played a remarkable innings and the way he approaches his game is fantastic. He got us out of the dangerous situation, full credit goes to him," Zaheer said about Laxman, who holds an impressive record against the Australia.
Asked if he thought that Laxman was a better candidate to be awarded man-of-the-match, he said, "I would have no problem if the man-of-the-match award had gone to him. As a team, we play to win, and that's what matter to me. I would rather give it to him. Winning matches is more important (than awards)."
Zaheer also agreed that the sight of Laxman batting on the field calms the nerves at the dressing room especially when the team was in a difficult situation.
Regarding Laxman's back spasm, Zaheer said he had talked to him at the end of the match today and the back stiffness was still there and the team physio was taking care of it.
On bowling on the Mohali track, Zaheer said for fast bowlers bowling in the sub-continent was always tough."But we fought hard and had a superb game of cricket over the five days. Both the teams wanted to win badly," he said.
Zaheer said that everyone inside the dressing room was a bundle of nerves when India were struggling to chase the target of 216 and with tail-enders batting with Laxman.
"Everyone was nervous for sure, I was also very nervous," he said.
Zaheer said the mood in the Indian dressing room when the match could have swung either way was that of nervousness but eased out later after the win.
"We were trying to be calm and maintain that composure… but I am sure everyone was nervous. This is what it is all about. You give your best shot and not think about the result," he said about the two teams desperately trying to snatch a win.
Zaheer said at the fall of Tendulkar's wicket his side knew that they need a decent partnership to stay afloat and it came from Ishant, who batted with great responsibility, and Laxman.
Asked if Laxman had been given injections or medicine to enable him fight his back pain, Zaheer said, "I don't want to get into it. The team physio could throw more light on that aspect."
On being asked if beating the Australians in a close game had given his team extra joy, he said, "We were lucky to win this game. Extra joy is there, but we will wait for the series to be over."
"We focus on the process and I am glad we won the match which has shifted the momentum in our favour. Hopefully, we should be able to do the same thing in Bangalore. Just focus on the process, prepare well over the next couple of days and give your best," he said.