"If we can work on the first couple of overs to him and stick to the plans a bit more, then hopefully we can put some pressure on him."
The plans certainly haven't been working so far. Gayle has provided the impetus in every innings and ensured the Windies' middle order has yet to be exposed with any regularity.
The New Zealand bowlers have picked up just 13 scalps from four matches on the tour, but Southee insisted the key to amending that record was the removal of one man.
"We firmly believe that if we get [Gayle] early we've got a very good chance of running through the rest of them and getting a score that we can chase down," he said.
"There's a few of their guys that haven't actually had a lot of batting, so if we can get a couple of early wickets then I'm sure we can make the most of that."
Despite boasting a one-day average just a shade below 40, Gayle had gone four years since his last century, also against New Zealand. In the intervening period, he spent a year away from the national team after falling out with the West Indian board before returning against England last month.
How the Black Caps must wish the impasse continued.
"He's obviously in some fine form," Southee said. "He's a serious player and can destroy any attack on his day. He's only human so it's not like we don't think we can get him out.
"He's scored the majority of their runs and he's been a massive influence in their success so far."
In saying that, today's success was also built around a run-a-ball century from Marlon Samuels. In reply, the Black Caps failed to replicate their hosts' example as Martin Guptill (51), Kane Williamson (58) and BJ Watling (72no) all notched half-centuries.
"I guess it's a step in the right direction but there's still a lot to work on," Southee said. "The batting was an improvement, it's just now we need a couple of guys that get in, to go on and get big scores."
One man with the potential to do that is Brendon McCullum, New Zealand's own destructive top-order batsman. He was rested from the limited overs series but he will arrive in St Kitts the day before game three and may be available.
New Zealand need a win on Thursday not only to keep the series alive but wrest some momentum away from the confident Caribbean side.
"We've still got a series to win and we firmly believe we can do that," Southee said. "We've got three games left and it's going to take a massive effort."