Anderson smashed three fours and four sixes in his 68 not out off just 40 balls after Kane Williamson (71) and Ross Taylor (55) had laid the groundwork for the left-hander.
Captain Brendon McCullum and Luke Ronchi acted as useful foils for Anderson as the Black Caps reached 292 for seven after being put in to bat.
Jesse Ryder wasted no time in taking the attack to India's bowlers, thumping the fifth ball he faced off Bhuvneshwar Kumar over square-leg for six.
He then slapped three fours off Mohammed Shami, who had the last laugh when he bowled the left-hander for a quickfire 18.
Ryder's opening partner Martin Guptill was a bit more circumspect but his patience wore out after an attempted cut off Shami flew to Ravichandran Ashwin at first slip.
Williamson and Taylor slowly set about repairing the damage although the former released the shackles with a clip through midwicket for New Zealand's first boundary in six overs.
Williamson was the more attacking of the two and brought up his 50 off 66 balls with a single down to long-on in the 26th over.
Taylor followed suit in the 33rd over and needed just 70 deliveries to reach his half-century, despite hitting just one four in his innings.
Williamson cut Ravindra Jadeja for four but perished in the same over to end a third-wicket partnership of 121 as he carelessly lifted the slow left-armer to Ajinkya Rahane at silly mid-off.
Taylor then wafted at Shami to be caught behind, although McCullum and Anderson quickly settled into their stride.
Ishant Sharma came in for some heavy punishment in the 40th over, with Anderson's six over the square-leg boundary followed by back-to-back fours from McCullum.
The New Zealand captain would depart for 30, though, as his opposite number Mahendra Singh Dhoni took a marvellous catch standing up to the stumps off Kumar.
Anderson and Ronchi took up the slack, however, with both players finding the boundary rope with alarming regularity as India conceded 39 runs in the 44th and 45th overs.
Anderson became the third home player to go past his half-century in the 47th over before launching Ishant over midwicket for his fourth six soon after.
Ronchi departed for a rapid 30 and although New Zealand failed to find the boundary rope in the final two overs, they kept the score ticking over to set India a tricky target of 293 for victory.