Left arm pace bowler Wagner was the 13th man added to the squad after impressing for the New Zealand XI in their victory over England in Queenstown and brought into the starting side when Doug Bracewell was ruled out with a cut foot to take the third seamer role.
The 32-year-old Martin, who was making his debut, had been expected to take the spinner's role until there were suggestions that New Zealand may instead opt for four pace bowlers at University Oval.
"Dougie's an awesome bowler and he's done well for his country. I don't know if that would have changed their decision," Wagner said when asked did he think he would have played if Bracewell was fit. "They may have gone in with four seamers or maybe still played the spinner.
"Obviously playing the spinner helped today, Bucko (Martin) bowled well taking four wickets himself which was pretty pleasing, especially on his debut."
Wagner had knocked the top off England's batting line-up, dismissing captain Alastair Cook, Ian Bell and the prized wicket of Kevin Pietersen leg before for a golden duck with a swinging delivery that would have cannoned into middle stump.
"Getting Kevin's wicket was massive in the warmup game but getting him in a test is even better," Wagner added with a smile.
"It's one that I would have liked and wanted if you asked me before the test, is there any wicket you really want, that was the one.
"We knew we had to try and make it count, first ball up make it swing and try and get ourselves in with a shot. I was just lucky that I got it in the right area and it swung and it happened.
"To have got that first ball up I was really pleased with that."
While New Zealand had been tidy with their bowling they were not really penetrating, with England's batsmen dismissed on poor shot execution, though Wagner said their attack had thought the brand of cricket the visitors play would lead to mistakes.
"They play a positive brand of cricket; they're a positive side and a good team," the South African born Wagner said.
There's days when it doesn't come off and days when it comes off and on those days you don't want to be the opposition and they can hurt you badly.
"Other days it doesn't come off and it was just one of those days when it didn't work for them.
"On the day we just executed what we needed to do and it worked for us. We're quite happy about that."
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