The veteran left-hander, who made 88 off 44 balls against Kenya on Friday, blasted 61 off 44 as Sri Lanka surpassed Kiwis 164-7 with seven balls to spare at the Wanderers.
Jayasuriya, the eldest player in the 12-nation event aged 38, gave his team a flying start by posting 82 for the first wicket with Upul Tharanga (37) off only 45 balls.
Jayasuriya, who hit six boundaries and three sixes, fell in the 18th over with just seven needed for victory and was named man of the match for the second day in a row.
Sri Lankan captain Mahela Jayawardene followed his 65 against Kenya with 35 not out off 18 balls with four boundaries and a six.
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It was the perfect practice match for Sri Lanka, who begin their Super Eights campaign against Asian rivals Pakistan here on Monday.
New Zealand, who have also qualified for the next round from group C at the expense of Kenya, clash with India at the same venue on Sunday.
New Zealand's innings revolved around Ross Taylor's 62 off 44 balls aft