Wood now has 30 goals for the All Whites in 62 matches, ahead of Coveny's 29 achieved between 1992 and 2006 (64 games).
More importantly, the result sealed qualification to the last four.
With one round to play in group B, the All Whites have six points, ahead of Fiji and Papua New Guinea (both three points), who face each other on the final match day.
With more of their regulars it was a much more cohesive display from the New Zealand.
Fiji defended stoutly, with plenty of numbers behind the ball, though New Zealand missed a number of first half chances – three fell to Wood himself – before the Newcastle striker opened the scoring.
More space opened up in the second half, as Fiji pressed for a goal, though Oli Sail was relatively comfortable throughout the match.
Danny Hay made seven changes to his starting XI, with only Oli Sail, Winston Reid, Clayton Lewis and Kosta Barbarouses retained from the 1-0 win over Papua New Guinea on Saturday. Tommy Smith and Nando Pijnaker joined Reid in a central back three, with Niko Kirwan and Francis de Vries employed as wing backs.
Marko Stamenic and Ben Waine were part of a midfield three, with Chris Wood leading the line.
From the outset, the match had a different pattern to the opening game against PNG. New Zealand enjoyed much more possession and width, while Fiji were prepared to sit deeper, soak up the pressure and look for opportunities on the counter attack.
Wood's presence made an immediate impact and the Newcastle striker had three great opportunities within the first 20 minutes. He slightly miscued a header from a Ben Waine cross, then held his head in his hands, as he hooked a left foot volley over the bar from six yards, after latching on to a rebound.
In the 20th minute he scuffed his close range shot towards the keeper, appearing to jar his right shoulder awkwardly as he fell, after Franco de Vries had headed back across goal.
There were further chances, with Marko Stamenic striking the outside of the post from distance, while Waine and Barbarouses also tested the keeper.
Fiji had defended well – physically and diligently – before New Zealand finally broke the deadlock on the stroke of halftime. Lewis got his delivery spot on from a free kick near the left touchline and Wood, for probably the first time in the half was left unmarked and made no mistake with his far post header.
After Wood and Barbarouses both eschewed chances, Just swivelled nicely to hammer home from a corner, after pinball in the Fijian box, for his first international goal.
Wood then grabbed his record – slotting home after Just provided the through ball – which was the impetus for Hay to begin rolling through his substitutes.
Lewis had the final say with well taken spot kick, after Logan Rogerson was fouled in the area.
Reid, Smith and Pijnaker were safe at the back, with Oli Sail acrobatically turning away Fiji's only attempt on target late in the second half.
All Whites 4 (Chris Wood 45', 73' Elijah Just 71', Clayton Lewis 90+3 pen)
Fiji 0
