Ruben Providence struck in the 12th minute at Inter Miami's stadium in Florida on Tuesday (Wednesday AEST) and substitute Lenny Joseph doubled the lead for the 82nd-ranked Caribbeans six minutes after the restart.
Frantzdy Pierrot grabbed a third with a header after the hour-mark before Markhus Lacroix finished the demolition job with a long-range rocket as the counter-punching Grenadiers dismantled the World Cup's lowest-ranked nation.
Haiti's build-up was overshadowed by visa trouble for midfielder Woodensky Pierre, the squad's only player based in the Caribbean nation.
Pierre was unable to play against the 85th-ranked Kiwis because his visa was not approved by US authorities until too late.
New Zealand skipper Wood became his nation's most-capped player with 89 appearances, moving one past Ivan Vicelich, but there was little to celebrate for the Nottingham Forest striker.
Wood conjured one of his side's few chances early in the first half with a bicycle kick, saved on the line by goalkeeper Jhony Placide.
Alex Paulsen had a poor audition to be the All Whites' starting goalkeeper, while centre back Finn Surman also had a first half to forget.
Both were culpable in Providence's goal as the Netherlands-based forward wriggled by Surman in the area and chipped Paulsen from a tight angle.
New Zealand coach Darren Bazeley put Max Crocombe in goal for the second half amid a slew of substitutions, but three goals sailed by the hapless keeper as the top Oceania nations' defence collapsed.
Joseph took a through ball between defenders Michael Boxall and Francis De Vries and tucked a left-footed shot into the corner before an unmarked Pierrot headed in a cross from five metres on 62 minutes.
Lacroix completed New Zealand's embarrassment on 87 minutes when he turned on the edge of the area and blasted into the right corner of the net, sending blue and red-clad fans into a frenzy.
