The pair shared an unbroken 117-run stand to take New Zealand to 152 for one at tea before it started drizzling at Kanpur's Green Park Stadium and no further play was possible.
Having bowled out the hosts for 318, New Zealand lost Martin Guptill (21) before lunch but the left-right combination of Latham and Williamson negated the home spinners with aplomb.
Latham was unbeaten on 56 with Williamson on 65 as New Zealand trailing India by 166 runs with nine wickets in hand.
"We were disciplined, we stuck to the gameplans. When the Indian bowlers missed, we jumped all over," New Zealand batting coach Craig McMillan told reporters.
"The way they rotated the strike, their left hand-right hand combination throughout the partnership was crucial."
Guptill could not convert the start he got and was trapped lbw by a full, swinging delivery from Umesh Yadav.
Latham and Williamson, however, looked comfortable against the spinners who did manage a few leg-before appeals but could not separate them.
The batsmen brought up their individual fifties in successive overs, but not before Latham had survived a scare.
He went for a sweep shot against Ravindra Jadeja and the deflection hit his boot and popped up for Lokesh Rahul to take the catch at short leg.
The decision was referred to the third umpire who ruled in the batsman's favour after replays suggested the ball had touched the chin strap of Rahul's helmet.
According to regulations, parts of protective gear must not come into play while taking a catch.
India's batting coach Sanjay Bangar said an early wicket was all the home team needed when play resumes on Saturday.
"It's a matter of getting that breakthrough and putting the pressure back on them," said Bangar.
"We were in a similar position wherein we were 150-odd for one at one point of time. Obviously when the ball starts to get older and the batsmen tire a bit, you get a breakthrough and it can be a different ball game."
Resuming on 291 for nine, the Indian tail wagged to take the hosts past 300.
With number 11 Yadav (nine) at the other end, Jadeja (42 not out) took the onus of scoring on himself, contributing 26 of the 27 runs India added to their overnight score.
Jadeja hit Mitchell Santner for a six but could not get to his second test half century as Neil Wagner had Yadav caught behind to end a 41-run partnership for the last wicket.
(Editing by Ed Osmond)
