There will be much greater tests to come for the All Whites in 2017, as the Fijian side looked disorganised at the back and struggled to utilise the pace and skill of Roy Krishna, but the result continues New Zealand's unbeaten run against Oceania sides under Hudson.
The three points gained mean a draw in the return match in Wellington on Tuesday evening will seal the All Whites' passage to the next phase, an Oceania final playoff in September.
In the first half Rojas had the ball in the net in the 32nd minute, after some incisive passing on the edge of the area, but the Melbourne Victory striker was judged offside.
It was a tight call, but looked the correct one.
Rojas was a constant menace, while Wood looked in confident touch off the back of his recent Leeds exploits. Clayton Lewis had the All Whites' first opportunity, with a stinging shot from outside the area in the 13th minute which was turned away well by the Fijian keeper.
After barely doing anything on attack in the first period - Fiji only ventured into the New Zealand half twice in the first 25 minutes - the home side came into the match in the 10 minutes before halftime.
They put the All Whites under some pressure near their own area, and only a superb Themi Tzimopoulos covering tackle prevented a Fiji goal after a swift counter attack.
Tommy Smith wasn't included in the starting XI in his return to international football, with the Ipswich defender coming on as a late replacement in the second half.