The hosts lost Williamson just before the final powerplay, paving the way for former opener and captain Brendon McCullum (30).
Shami dismissed Taylor early in the powerplay but New Zealand still managed to score 41 off the five overs.
That set the stage for Anderson, who recently displaced Pakistan's Shahid Afridi as the holder of the record for the fastest hundred in ODIs.
Anderson bludgeoned his way to a half-century in just 30 balls. New Zealand benefited immensely as Anderson and Luke Ronchi (30 off 18 balls) combined well to rack up 50 runs off just five overs.
To their credit, however, India managed to limit the damage by bowling full-length balls well outside the off-stump. The tactic worked in keeping Anderson quiet in the fag end of the innings.
Bhuvneshwar Kumar, who picked up a solitary wicket, was the most economical of the Indian bowlers but Shami was the pick of the bowlers, taking four wickets for 55 runs in his spell of nine overs.
