Pujara, making a comeback to the Test side after a long time, was unbeaten on 135 as he saved the Day 2 of the third Test against Sri Lanka.
"He has a tight technique and temperament to get out of tough situations. He is someone who is not ruffled when beaten around off stump. He would say okay, this is your time but my time will come after some time," Gavaskar said.
Now that Pujara has done well while opening the innings, India have a lot of choices for the opener's slot. Shikhar Dhawan and Murali Vijay are out due to injury and young KL Rahul has made his case with century in second Test.
"They (Vijay and Dhawan) will resume (get their places) back and it is a good headache to have for selectors. The problem of plenty is better to have than having no one to choose to from," the former opener said.
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Gavaskar said both skipper Virat Kohli and Rohit need to be patient when the conditions are tough.
"Virat has gone back to pushing hard at deliveries outside off. He was playing a ball on the 6th, 7th stump. He likes the ball to come to him at speed but when the ball is moving he reaches out to the ball and that's his problem."
However he said Stuart Binny actually faced "good" balls when he got out but he needs to do well with the ball to keep his place in the side.
Gavaskar said Naman Ojha, who made is debut, needs to be careful with his shot selection at this level.
"If it is his natural game and not much can be done. It's different getting runs in first class cricket and at Test level."
Gavaskar said if weather does not interrupt, there will be a result in this match and India have got themselves into a "very good position.