Then, yesterday, Bangalore was treated to the best Southee has bowled in his career.
With the match evenly poised, New Zealand needed to get rid of the established Virat Kohli and M.S. Dhoni to have a chance of claiming a lead.
Southee did just that, removing Kohli for 103 in his second over with the new ball before dismissing Dhoni for 62 in his next turn at the crease.
And he wasn't done. In his next over he picked up Ojha and Zaheer Khan to leave India with their last wicket.
He would have had that, too, had Guptill taken a chance at second slip that was tough, but by his high standards, very catchable.
Instead, Southee settled for career-best figures of 7-64, the 23-year-old's second five-wicket bag in tests. The haul was the sixth-best by a New Zealander in history, and if Guptill had grasped the edge from Ravi Ashwin, Southee would have trailed only Sir Richard Hadlee's 9-52.
"It's up there," Southee said of the stretch in which he claimed four wickets in 15 balls.
"They're tough bowling conditions in India with not a hell of a lot of bounce in the wicket, but it was nice to have the new ball in my hand and swing it a little bit.
"It was one of those spells you'll remember for a while."
The spell leaving Southee surrounded by illustrious company in the New Zealand record books, he could even afford to forgive Guptill for his flub in the field.
"It happens - it was a tough chance," he said. "It would've been nice to grab that one but that sort of stuff happens in cricket.
"I'm happy with the seven."
On what has been a pretty good pitch for batting at M. Chinnaswamy Stadium, Southee had no inkling when he came to the ground yesterday of what was to follow.
He bowled as if he had a point to prove, as if he had to keep up with the strides made by junior pair Doug Bracewell and Trent Boult in recent tests.
Southee replaced Chris Martin for this match, and the young triumvirate took all 10 Indian wickets.
"The group of us are very tight," he said. "With Chris - he's been instrumental in the bowling department for the last 10 years - it's never easy when someone misses out."
It's safe to say Southee won't be the one missing out the next time New Zealand wear the whites.
And if they go into that test, in Sri Lanka later this year, with a recent win under their belts, Southee will probably be the main reason why.