The spin duo bowled out South for 305 in the second innings to set star-studded North, who led by 162 runs on the first innings, a comfortable victory target of 144.
At stumps North were four for none with Gautam Gambir (4) and Virender Sehwag (0) at the crease.
In the morning North lost their remaining wicket after adding three runs to be all out for 500 in the first essay, in reply to South's 338.
Trailing behind North, South suffered an early blow when they lost opener Robin Uthappa, top-scorer in the first essay, cheaply. He was trapped leg before by left-arm paceman Ashish Nehra for zero in the first over itself.
The 150-run partnership for the second wicket between Swapnil Asnodkar (74 with 11 fours) and Sridharan Sriram (80with 15 fours) provided some stability to the innings before the latter was caught behind off Amit Bhandari.
Skipper Venkata Sai Laxman, who made his second half-century of the match (59 with six fours and a six), then combined forces with Asnodkar to take the score ahead. But once this partnership was broken, off spinner Harbhajan and leg-spinner Mishra were unstoppable.