Shami and fellow senior pacer Ishant Sharma were rested from the Oval Test that India won by 157 runs to take a 2-1 lead in the five-match series as the duo was nursing niggles.
Rohit Sharma added a crucial 153-run stand for the second wicket alongside Cheteshwar Pujara, who made 61.
It took eight years and 43 Test matches to get an overseas hundred and that too in England in tough conditions, and there won't be any second guess about where this knock of Rohit will rank among his eight tons.
India are currently leading the five-match Test series 1-0 with two days left in the third Test at Headingley.
By stumps on the third evening, India reached 215 for two in their second innings courtesy Pujara and Rohit (59), with the former only 9 runs behind a century.
Cheteshwar Pujara was batting on 91 and giving him company was skipper Virat Kohli on 45. Opener Rohit Sharma got out after scoring 59.
Pujara has been a hot topic of discussion amongst Indian fans and critics for his slow batting in Test cricket.
Rahane even laughed off the flak they faced on social media by saying that only "important people" are talked about.
The experienced duo of Pujara and Test vice-captain Rahane have not been at their best of late, averaging in the 20s this year.
With Kohli wanting to stick to his template, focussing more on picking 20 wickets, the middle order needs to deliver in what arguably stands India's best chance to win a series in England.
Gavaskar described Rahane and Pujara as "low-profile" cricketers and said that questions must be asked of the support staff if both the players are getting out in a similar fashion.
Shaw, who has represented India in five Tests and three ODIs, is part of the national squad in Colombo selected for the limited-overs series against Sri Lanka, starting July 13.
In an exclusive conversation with India TV Cricket, former cricketer Vivek Razdan talked about the importance of Cheteshwar Pujara, Ajinkya Rahane's style of batting in Test cricket.
Pujara's last Test century came in January 2019, during India's historic series win in Australia.
The world's top run-getter across Tests and ODIs said the Blackcaps were the superior team.
Earlier, New Zealand managed to eke out a 32-run lead in the first innings after pacer Mohammed Shami's four-wicket haul (4/76) curbed them to 249 in the rain-marred clash.
Pujara's strike-rate has been a constant subject of debate for sometime now and the India No. 3 did his stats no good on Saturday, scoring 8 off 54 balls.
Even Gill was hit on the helmet when he was up against Jamieson. The play was stopped for a few minutes while he was checked for signs of concussion.
One of the shining products of the traditional format, Pujara made no bones in admitting that playing the WTC final against New Zealand is a "big deal" for him even though he would try to treat it as another game of cricket.
Earlier in the day, the official Twitter handle of the BCCI had shared a video of a nets session at the Hampshire Bowl.
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