Lose and they should still be okay, providing it's not a belting and Mumbai Indians don't pummel Perth the following night.
Both teams reached 167 yesterday. Neesham stood up yesterday at a time Otago were on shaky ground, hitting an unbeaten 52 off just 25 balls, then helping take 14 off the Super Over, then bowling Otago's response.
The 23-year-old kept his head after the Lions century-maker, Quinton de Kock, clobbered 10 off his first two balls. The celebratory hugs at the finish had more than a hint of sheer relief about them.
Lefthander Neesham has hit 113 runs off 61 balls in the tournament. He has played six games for New Zealand, three of each short form. His Otago coach is convinced there are many more to come.
"This kid will play a lot of international cricket," Vaughn Johnson said.
He hits a long ball, is a handy medium pacer and is capable of fielding brilliance, best exemplified by a spectacular running, leaping catch at long on to dismiss Henry Davids at East London last December.
The win is Otago's 15th on the trot, second only to Pakistan's Sialkot Stallions' run of 25.
The key has been players stepping up to take responsibility.
"I guess today it was just my turn," Neesham said.
Neil Broom's maiden T20 century against Perth was ideal timing; veteran seamer Ian Butler is the leading wicket taker with eight; hired gun Ryan ten Doeschate has a strike rate of 200 from four innings and Brendon McCullum is yet to fire in the tournament proper.
Neesham backed captain McCullum's faith in him.
"It's your night, have a go," was how he described McCullum's Super Over logic.
New Zealand's tour of Bangladesh will be screened live on Sky Sport. The tour includes two tests, three one-dayers and one T20, starting on October 9.