The six was hit by Afghan batsman Asghar Stanikzai.
Tui spokesman Simon Smith said Mr Gough, a married father of two, was numb following the catch.
"He said he hasn't played cricket for a while and didn't know if he could catch one.
"He [thought] he'd be able to catch one because he was so high up in the stand."
Mr Gough is the third person to nail a qualifying catch.
Auckland man Travis Committie, 23, snared a six off JP Duminy's bat during South Africa's clash with Zimbabwe at Seddon Park last Sunday, and Canterbury man Sunjay Ganda caught the first qualifying six during the opening match of the Cricket World Cup.
In Wellington on Friday, Jason Bragg missed out on a share of the prize when Tui determined he had made a "fumble" when he caught a ball off a six from Brendon McCullum in the match against England.
Mr Gough said it was a "stupid chain" of events that led to the catch.
"We got given the tickets by my wife's friend, and then I was actually going to stay at home with our son and come down a bit later because I got to go to the Scotland game alone because my wife couldn't get off work.
"I said, 'You go first and I will bring the wee guy down later.' She said, 'No you go and try and catch the ball. If you catch it we can have another wedding.'
"We had basically just got in and sat down. I said to my daughter, 'We're actually quite far back here, I don't know if we will get one up here.'
"It must have been the first ball I paid attention to about 30 seconds later. I remember thinking, 'That's coming in our direction, actually that's coming right at me.'
"I was actually quite lucky because there was quite a lot of space around me. I moved to my left so I could use my right hand. When it was about 10m away, I was thinking, 'Oh my God, don't drop it'."
