He earlier removed the dangerous Tillekaratne Dilshan, with a ball which bounced a touch more than expected and produced a gentle return catch.
"They were massive wickets," Anderson said. "He's just so good. It's pretty easy to sum him up. He's smart and knows how to get guys out."
Vettori finished with two for 34 from his 10 overs demonstrating his immense value to the side.
Anderson picked up two as well, to follow a rampaging 75 off 46 balls, which was a major part of New Zealand pushing on to 331 for six.
He revealed there was no chest-thumping pre-game team talk from McCullum, which fits the skipper's low-key attitude to this World Cup.
"He spoke the day before the game and said he wasn't going to give any motivational speeches, just treat it as another game and go about our work. Keep what we've begun as a juggernaut rolling forward.
"He does have a massive calming influence on the dressing room. We all know with Baz that, when it's a big event, he really turns it on."
Anderson believes New Zealand have received a bonus by facing Lasith Malinga at the start of the World Cup, when the Sri Lankan spearhead is sorely underdone after a five-month break with injury.
Malinga was towelled yesterday, with 84 coming off his 10 overs. But Anderson has been a team-mate of Malinga's at the Mumbai Indians.
"I've been lucky to face him at Mumbai in the nets. I guess he's only a couple of games back so he'll be better for that run and we're probably lucky we faced him early on as well. I imagine he could start tearing teams apart later on."
Three things we learned
• In nine completed innings batting first this season, New Zealand have scored 275 or more on six occasions and won each time. In the other three, they scored less than 250 and lost.
• With an innings of 39, Kumar Sangakkara became the second highest run-scorer in ODI cricket. He has 13,736 runs (at 40.99 and strike rate of 78), overtaking Australia's Ricky Ponting (13,704 at 42.03 and a strike rate of 80). India's Sachin Tendulkar leads with 18,426 at 44.63 and a strike rate of 86.
• Lasith Malinga's figures of none for 84 from 10 overs are his fourth-most expensive in 172 ODI innings.
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