Unfortunately for New Zealand, that completed the complement for the three seamers, and with Todd Astle (0-34 from three overs) having taken some punishment, stand-in skipper Southee turned to Daryl Mitchell for the final over.
Given the unenviable task of defending 10 runs in front of a rabid home crowd, a player with only 11 overs of T20I bowling experience conceded two wides and a game-sealing boundary to Rishabh Pant.
That meant an impressive knock from Mark Chapman (63 from 50 balls) counted for little, the 27-year-old shining in his first appearance since April and sharing in a 109-run stand with Martin Guptill (70 from 42).
The junior partner in that pair hit his first T20I half century for New Zealand and equalled his previous best international score, recorded while playing for Hong Kong in 2015.
After New Zealand were sent in and Mitchell had been removed for a duck, Chapman was aggressive in moving around the crease, initially struggling for timing but soon monopolising the strike and building on a slow start.
He helped the Black Caps reach 65-1 at the halfway mark, registering his 50 with a second six before being deceived by the flight of Ravi Ashwin and having his off stump rocked.
"It wasn't ideal losing Daryl in the first over," Guptill said. "But the way Chappy adapted to having not played a lot of cricket lately, coming in and spending some time in the middle, to put on a hundred partnership with him really helped the team get to a competitive total."
A few imperious blows from Guptill also aided in that aim but his wicket, coming at 150-4 in the 18th over, saw New Zealand limp home and manage only 20-3 from the final three overs.
"We were still 10 runs short of where we could have been," Guptill said. "I don't think we quite nailed the end of the death phase as well as we could have, but that can happen."
That shortfall was especially obvious when contrasted with India's fast start, as Rohit Sharma (48 from 36) attacked both Boult and Southee to help his side race to 50-0 after five overs.
Mitchell Santner (1-19) reined in the hosts by removing KL Rahul with his first ball, but India were still finding the fence with enough frequency to be in control at the halfway mark, needing 80 more on a good surface for batting.
Suryakumar Yadav brought up 50 with a towering six and, needing wickets to have hope, the Black Caps saw a big chance slip through Boult's fingers on the fine-leg boundary. Boult would get some revenge from the bowling crease, dismissing Yadav for 62, but the late fightback was barely insufficient.
"The bowlers did an extremely good job to pull it back after they got off to a fairly quick start," Guptill said. "To lose with only a couple of balls to spare, we weren't far off.
"I don't think we've played bad cricket in the last two games - we've just come out on the wrong side."
