The 32-year-old's 74th worldwide goal delivered a win over Russian Federation on Wednesday, meaning a draw against the pointless Kiwis would be enough for the Euro 2016 champions to advance to the last four.
The top two teams go through to the semifinals, and with Russian Federation playing Mexico in Kazan, also on Saturday, Fernando Santos' team can reach the knockout stage by securing a draw against the All Whites.
Although Mexico dragged themselves back into the game and scraped the win due to goals from Raul Jimenez and Oribe Peralta, the Kiwis nearly leveled when midfielder Ryan Thomas rattled the crossbar in the closing stages.
"Everyone is incredibly disappointed in the changing room and we feel we should have got more", said Hudson.
Portugal coach Fernando Santos has paid the All Whites the highest possible compliment, saying that the current New Zealand team has the capacity to surprise anyone.
"It's less than 72 hours to recover, it's not easy", said the coach, who steered his team to the Euro 2016 title over seven games in a 27-day period in France.
With the Confederations Cup in full swing over in Russia, New Zealand took on Mexico in Sochi on Wednesday night, having lost 2-0 to Russia over the weekend. We really needed the three points and winning tonight put us in a very good position.
North Korea denies USA claims that Otto Warmbier was tortured
United States doctors said Mr Warmbier had suffered a severe neurological injury from an unknown cause. He was sentenced to 15 years of hard labor for committing " hostile acts " against the state.
"On paper they seem better than us".
With star striker Javier Hernandez on the bench, Mexico's three-man attack of Peralta, Jimenez and Juergen Damm struggled to make an impact early on.
New Zealand should not be underestimated, however, especially as they will be in confident mood on the back of their encouraging performance against Mexico in Sochi on Wednesday.
The Oceania champions took a shock lead when Clayton Lewis threaded his pass between two defenders to Wood, who coolly fired home on 42 minutes.
While acknowledging Ronaldo's status, New Zealand manager Anthony Hudson was keen to stress that even without him, the European champions will pose a serious test for his already-eliminated side.
"If we play like we did the other night, I have all the confidence in the world".
At the other end, Wood squandered a one-on-one with Talavera and moments later Mexico were level. "But it's a 90-minute game and we have to have a look at what happened during the second half", he added. Not surprisingly, this all led to a classic brawl, with ref Bakary Gassama turning to the Video Assistant Referees to sort it all out.
- National Oilwell Varco, Inc. (NOV) Downgraded to Sell at ValuEngine
- Leeds Rhinos 12-23 Castleford Tigers
- CytRx Corporation (CYTR) closed its previous trading session at $0.69
- Nancy Pelosi: 'I'm worth the trouble.' Conservatives agree
- Cristiano Ronaldo remains coy about his Real Madrid CF future
- Noose tightens: Russian Federation fires missiles at Daesh from Mediterranean
- Funeral to be held for U.S. student imprisoned by N. Korea
- Remaniement : les grands travaux du nouveau gouvernement
- New Orleans Friday weather: Mostly cloudy, 50 percent chance of rain
- Watch The Vertical NBA Draft LIVE