India's Pujara (114 not out) refused to bow to the pressure applied by Panesar in the first two sessions at the Wankhede Stadium, where England are seeking to bounce back from their nine-wicket defeat in Ahmedabad.
In his first Test for eight months Panesar took four for 91, including the wickets of Virender Sehwag and Sachin Tendulkar but he could not shift Pujara, England's chief tormentor with an unbeaten double-century last week and the principal reason why they could not press home the after-noon advantage of 119 for five as India closed on 266 for six.
On a pitch which favoured spin from the outset, and with England scheduled to bat last, the hosts' recovery may prove telling.
Left-arm spinner Panesar said: "I thought we stuck at it really well. We put a lot of pressure on India early doors, which is something they probably didn't expect. They won the toss, looked to have a bat and probably thought maybe they'd only have a few wickets down for 200-plus but we applied a lot of pressure to them and having five wickets down really early was a testament to how we did that."
Panesar concedes Pujara, specifically in his unbroken partnership of 97 with Ravichandran Ashwin (60 not out), has regained some ground.
"They obviously built a really good partnership. What we're hoping is we can restrict them to under 300," Panesar added.
"That kind of partnership has given a bit of momentum to the Indian innings, but overall I don't think they expected us to dominate the first two sessions like that."
Ashwin had some ominous observations for England.
"There's a lot more bounce," Ashwin said. "I don't think you can really plonk your foot forward and keep defending. There's definitely more aid for the spinner, whereas Ahmedabad was low and slow.
"When it starts spinning [here], it does go, it's quite a tough wicket to bat on.
"At this point in time we've got to a position where we can feel a little comfortable . . . if we can get a more runs I think we can put a lot of pressure on them."