The tourists cantered to an easy seven wicket victory in the opening match in Napier on Thursday, overhauling New Zealand's 285-8 with 10 overs to spare.
Veteran opener Sanath Jayasuriya did most of the damage, smashing 111 runs from just 82 balls against a wayward attack missing most of New Zealand's frontline bowlers.
Vettori, who is replacing regular captain Stephen Fleming for the first two one-dayers in the five match series, told reporters Saturday that New Zealand's bowling attack needed to get the basics right.
"The bowling plan is exactly the same, it's just about the implementation, which we let slip in Napier," he said.
"Sri Lanka bat down to seven and eight, so you've got to take wickets at the top and try not to buy those wickets, which we tended to do in the first game."
Another potential hurdle for the home side could be the loss of experienced batsman Nathan Astle, who suffered bad bruising to his thigh as he returned to form with 83 runs in the series opener.