Peter Fulton dropped a catch in the fourth over, putting down Powell on eight after Southee drew an edge from the lefthander.
Replay: Live chat with Jimmy Neesham
Neesham v Anderson dilemma
Neesham scored his debut ton (137 not out) against India at the Basin Reserve in Wellington at the start of the year. He batted alongside Brendon McCullum in New Zealand's second innings of the test as his skipper became the first New Zealander to reach 300.
Watling also scored a century in that innings against India, his third, putting on a record sixth wicket 352-run partnership with McCullum.
From the archives:
Neesham makes own history on debut
Benn (3-142) and Shane Shillingford (3-145) were the pick of the West Indies bowlers with six of the New Zealand wickets falling to spin.
In the morning session, New Zealand's No. 3 Kane Williamson, who dominated day one with his sixth test century, eventually went to Benn for 113.
Former skipper Ross Taylor, overnight 34, scored a resolute 55 at Sabina Park.
Earlier, Williamson and Taylor patiently stretched their third-wicket stand to 85 in the first 45 minutes before Benn knocked back Williamson's off stump as the batsman played no stroke. Williamson hit 12 fours off 298 balls.
Shillingford soon added the scalp of Taylor, who chipped an ondrive to Kirk Edwards at midwicket. Taylor hit eight fours in just under three hours.
New Zealand quickly dipped to 279-5 when Benn got one to turn and bounce. McCullum's edge went to Chris Gayle at slip via the shoulder of wicketkeeper Denesh Ramdin.
Centuries in first two tests
Bill Ponsford (Australia) vs England, Sydney and Melbourne, 1924-5
Doug Walters (Australia) vs England, Brisbane and Melbourne, 1965-66
Alvin Kallicharran (West Indies) vs New Zealand, Georgetown and Port of Spain, 1972
Mohammad Azharuddin (India) vs England, Kolkata and Chennai, 1984-85
Greg Blewett (Australia) vs England, Adelaide and perth, 1994-95
Sourav Ganguly (India) vs England, Lord's and Notthingham, 1996
Rohit Sharma (India) vs West Indies, Kolkata and Mumbai, 2013
Jimmy Neesham (New Zealand) v India and West Indies, Wellington and Kingston, 2014
- With AP