The 25-year-old then returned to New Zealand and scored a hat-trick in the All Whites' 6-1 win over the Solomon Islands in the first leg of their World Cup qualifying clash.
Burnley struggled to create further chances for Wood on Monday (NZT), conceding the greater share of possession and territory to their opponents.
However, the All White front man's predatory instinct proved the difference as he became the first player in Burnley history to score in his first two EPL matches.
It was the STG15 million ($NZ27.3m) signing's first start after having made 11 subsitute appearances in the EPL, firstly with West Bromwich Albion and then Leicester City.
Burnley manager Sean Dyche says Wood proved a crucial figure as Burnley struggled for their best.
"It's our worst performance of the season so far but the shape of the team, the belief in each other, was on show," he said.
"Chris Wood has made a good start and he scored a hat-trick for his country in midweek as well. He has a desire to prove himself in the Premier League. It was a great finish."
Wood is just the second player from Oceania to score in their first start in the Premier League - the other was Australian Brett Emerton in August 2003 for Blackburn against Wolves.
Wood is the sixth New Zealander to start an EPL match after Ryan Nelsen, Winston Reid, Simon Elliott, Danny Hay and Lee Norfolk.
Burnley's next match is away to English giants Liverpool - who sit a place below them on the table - next weekend before they face Wood's former club Leeds in a midweek EFL Cup fixture.