The 24-year-old Bhatia notched up 139 in 206 balls, studded with 14 fours, to help MP pile on runs after resuming on overnight score of 338 for five.
MP finally declared at a mammoth second-innings total of 560 for 9, just before tea on the fourth and penultimate day.
Bengal, who conceded a huge first-innings lead of 227 after being bowled out for a meager 121, are on the verge of a defeat as they were struggling at 113 for three in 31 overs at the close of play.
Their most experienced batsmen -- captain Manoj Tiwary (32) and wicketkeeper Wriddhiman Saha (6) -- were at the crease.
The batsmen out were first innings top-scorer Abhimanyu Easwaran (16), who top-edged a pull and was caught at square leg off MP pace spearhead Ishwar Pandey, his opening partner Sayan Mondal (39 off 86 balls) and Sudeep Chatterjee (16).
It will need a monumental effort from Tiwary and Saha if Bengal are to avoid an outright defeat.
MP were already ahead of Bengal by a huge 565 runs and decided to deny Bengal even the slightest chance of a comeback by continuing to bat resolutely.
Bhatia and Dane, who were on 18 and 14 last evening, added 149 runs for the sixth wicket before the latter was dismissed by part-time spinner Easwaran for 69 off 104 balls.
At lunch, Bhatia was six short of his hundred and completed it soon after the break, but MP showed no signs of declaring their innings till they lost their ninth wicket with 10 minutes left for tea.
Bhatia finally departed after a stay of 314 minutes, giving left-arm spinner Pragyan Ojha his second wicket of the innings.
Brief scores:
Madhya Pradesh: 348 & 560 for nine decl (R Patidar 137, Harpreet Bhatia 139; A Dinda 2/92) vs Bengal: 121 & 113 for three (M Tiwary 32 not out).
Image: Bengal captain Manoj Tiwary faces a herculean task to save his team from exit against Madhya Pradesh in the Ranji Trophy quarterfinal.
Photograph: Getty Images
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