Rookie opening bowler Andy McKay and Ian Butler helped restricted the tourists to 183 for eight.
McKay bowled superbly, taking two for 17 from 10 overs, and Butler picked up three wickets.
Ross Taylor helped make light work of the chase with a punishing 78 off 52 deliveries as the home side cantered to victory with more the 20 overs up its sleeve.
But the Black Caps did not have it all their own way.
Mushfiqur Rahim top-scored with 86 and led a fight back which saw the visitors score 92 runs from the last 10 overs - more than half the team's runs.
"Apart from our death bowling, it was another [good] all round performance," Vettori said"This is another ground you need 300 on to compete.
So to restrict them to 183 and have them 46 for six was pretty pleasing."
It is nit-picking, but Vettori acknowledged it was the little things which could prove damaging against better sides.
"The size of the [University Oval's] boundaries make it a little more difficult but still I think we missed too much. If we want to compete against Australia, it is an area of our game we have to make sure is almost perfect. Otherwise, it is difficult to stop very good teams."
Taylor claimed the man-of-the-match award for his knock but McKay must have been a close second.
"I was really impressed with the way Andy McKay bowled in his second game. He took the new ball and bowled with some pace and consistency. He did a great job today," Vettori said.
Bangladesh captain Shakib Al Hasan believes his side has made some improvements but still has plenty of work to do before the third and final match in the series, in Christchurch on Thursday.
"We are making more mistakes than we are improving," he said. "Every game someone is getting a start and getting runs but we need three or four guys to get runs to get a good total."
