But he allowed himself to be persuaded - eventually - by Michael McGlinchey, putting the team's desire for a goal ahead of possible personal glory.
"He's had a free kick just before, Woodsy, and I said to him 'I think this is maybe more my range, a bit closer in'," said McGlinchey. "He said 'nah, I'm on a hat-trick, I'm having it'. I said, 'look, let me have it' and he said 'ah, OK' and I put it in the top bin."
McGlinchey's shot was near perfect, essentially killing off the tie.
"I knew I was under pressure because he was [saying] 'I'm on a hat-trick' [and] standing over the ball. [But] we had that discussion and he let me have it."
The 25-year-old also grabbed another slice of New Zealand football history on Friday night, moving up to third on the all-time scorers' list for the All Whites, past a couple of legendary names.
Wood (23 goals) trails only Shane Smeltz (24) and Vaughan Coveny (29), after going past the late Steve Sumner (20) with his first and Brian Turner (21) with his delightfully chipped second.
"I'm sure when I finish playing [that] will mean a lot more but for now, it's not about that," said Wood. "My goal and the team's goal is the [2018] World Cup. We need to take that a step at a time and that comes with Tuesday."
There was an element of fortune in the lead-up to his first two goals but both finishes were top class and the 25m free kick for his third underlined his confidence.
Solomon's coach Felipe Vega-Arango admitted his game plan had centred around blunting the Burnley striker.
"My plan was simple," said Vega-Arango. "Five at the back, one of them, man to man cover [on Wood]. It's the only thing you can do. He plays in the Premier League, [he] just signed a huge contract and the other day at Wembley, [he] scored a equalising goal against Tottenham. We are talking about Tottenham, not Solomon Warriors, with all my respect to Solomon Warriors, and we didn't do the job. It's tough; you want to stop him but how do you stop him?"
Wood also stood out for his all-round play. His vision was one step ahead of most on the field, and he rarely wasted a pass. The skipper also worked hard, at one stage tracking back close to his own penalty area to win the ball.
"He was exceptional," said team-mate Ryan Thomas. "He has a busy schedule now [so] coming in, having three or four days to train and scoring a hat-trick like he did, it was very good for us."
His haul was just the second All Whites triple in more than a decade, and the first since Wood hit three against the same opposition in Honiara in 2012.
Wood won't have a chance to add to his goal-scoring tally in the return leg on Tuesday, with coach Anthony Hudson deciding to release Wood and Thomas back to their respective European clubs.
"We have the players within this group to win the game and finish the job," said Hudson.
