India will have to settle for the third spot behind England in the ICC Test team rankings after the latter managed to salvage a draw in the final Test against New Zealand in Auckland on Tuesday.
Matt Prior produced a belligerent century to ensure England saved the series-deciding third test against New Zealand at Eden Park on Tuesday.
Williamson picked up two wickets in the last session on Day 4 to leave England struggling at 90/4 at stumps, chasing 481 against New Zealand at Eden Park on Monday.
After bowling out England for 204, hosts New Zealand were reduced to 35 for three in their second innings at the close of play on the third day at Eden Park.
England's Jonathan Trott on Saturday surpassed Indian batsman Vijay Manjrekar in scoring the most number of runs in Test matches without hitting a six.
Trent Boult picked up his second wicket by dismissing Jonathan Trott for 27. England to 50 for 2 at stump on day two in third and final Test Against New Zealand at Auckland on Saturday, trailing by 399.
Peter Fulton (124*) and Kane Williamson (83*) guided New Zealand to 250/1 at stump on the opening day of the third Test against England at Eden Park on Friday.
New Zealand and England face off in a winner-takes-all third and final Test tommorrow, with the tourists striving for a series-clinching victory despite the absence of star batsman Kevin Pietersen.
Doug Bracewell will be added to New Zealand's squad for the third Test against England if he can prove he is match fit, coach Mike Hesson said on Tuesday.
Persistent rain and a pitch that offered the seam bowlers little assistance ensured the second Test between New Zealand and England at the Basin Reserve ended in a damp draw.