Prior (57) was the first of the sixth-wicket pair to twin 50s, defying the physics of this deathly slow Nagpur pitch to bag a trademark square-cut off Pragyan Ojhan for his sixth four.
But it was 21-year-old Root (65no) who was to play the most substantial innings on a surface which means every run is hard-earned.
A surprise inclusion for this match which England must at least draw to complete a historic series victory here, the young Yorkshireman needed 154 balls to pass his 50. There were only two boundaries along the way, in a nonetheless convincing innings which hinted at his significant potential at Test level and extended to 200 deliveries by the time he batted through a second successive session.
Root's was a telling performance too in the context of the match, after he and Prior joined forces on a vulnerable 139 for five on Thursday.
Their first task on Friday was to negotiate another spell from Ishant Sharma, in these extreme conditions which have made India's solitary seamer a bigger threat than any of their four spinners.
There were no scrapes against any of the bowlers, as England's batsmen kept their patience and tailored shot-making to the limitations of the pitch, until Prior succumbed to Ravichandran Ashwin.
The off-spinner struck, from round the wicket, with a delivery that did not turn but snaked past Prior's defensive push on the angle to hit off-stump.
Mahendra Singh Dhoni sensibly turned straight back to Ishant (three for 47), to attack the new batsman, and that obvious switch worked when Tim Bresnan missed an inswinger to go for a second-ball duck.
This was a pitch which did not appear likely to suit Graeme Swann's natural timing and clean-striking. But England's number nine confounded that premise to keep Root company for the remainder of the morning.