Southee took his six wickets in the series, including 4-36 in the final match to lift 15 places to a career-best 38th.
New Zealand captain Daniel Vettori kept his spot at the top of the rankings.
Shane Bond, who bagged nine wickets against Australia, has moved past injured teammate Kyle Mills to fifth, with Mills now sixth.
Bond is seven points behind fourth-placed Nuwan Kulasekara of Sri Lanka.
Taylor returned to the top 20 after improving his batting ranking by four places. He is now 18th, after scoring 177 runs in the series.
Scott Styris, who scored 199 runs against Australia, climbed three places to 37th, while second-ranked Australian Michael Hussey narrowed the gap to ranking leader Mahendra Singh Dhoni of India to just eight points after scoring 198 runs in the New Zealand series.
New Zealand opener Brendon McCullum dropped one place to 19th.
Australia fast bowler Mitchell Johnson returned to the top 10 after he took 12 wickets in the series to lift him four places to 10th.
He became Australia's highest-ranked bowler after Doug Bollinger slipped two places to 14th spot after managing just four wickets in the five ODIs.
