Franklin and Nicol scored fifties while Williamson hit a crucial 20 off 5 balls to help New Zealand chase down a target of 201 in last over against Zimbabwe at Hamilton on Tuesday.
Kiwis made two changes, resting opener Martin Guptill who has made half tons in his last five innings and naming Southee in place of Bracewell.
Martin Guptill continued his rich vein of form against Zimbabwe as he scored 91 not out to help New Zealand beat the visitors by seven wickets.
Brendan McCullum smashed his fourth one-day international century off 79 balls as New Zealand completed a sweep of their three-match series against Zimbabwe with a 202-run victory at McLean Park in Napier on Thursday.
Opener Rob Nicol plundered 146, the fifth highest one-day international score by a New Zealand batsman as they trounced Zimbabwe by 141 runs in the second one-day international on Monday.
Zimbabwe captain Brendan Taylor won the toss and elected to bowl in the second one-day international against New Zealand at Cobham Oval on Monday.
Discipline with the ball and aggressive leadership from captain Brendon McCullum have seen New Zealand secure an emphatic victory over Zimbabwe in their three-match one-day series in the first one-day international on Friday.
The last time these two sides played fifty-over cricket was against each other, in October last year.
After scoring 495, the Kiwis bowled out Zimbabwe for 51 and 143 to win the one-off Test by an innings and 301 runs to register their biggest victory margin.
New Zealand Cricket today announced a 14-player One Day International and Twenty20 squad for The National Bank Series against Zimbabwe.
