The Magpies man broke Vaughan Coveny's All Whites record last week, when he scored twice against Fiji to take him to 30 goals from 62 caps, and followed that up with another brace against New Caledonia a few days later.
And on Wednesday, he netted again in a 5-0 victory against the Solomon Islands, heading home in the first half and playing for 84 minutes in Doha.
The result keeps alive New Zealand's hopes of a first World Cup finals appearance in 12 years as 30-year-old Wood looks to make even more history for his country, who will meet the fourth-placed team from the CONCACAF region in an intercontinental play-off in June.
Wood - who also captained the All Whites on Wednesday - will now return to Tyneside ahead of Newcastle's game at Tottenham on Sunday.