But Wood’s double wasn’t enough for the Lions, who squandered a three-goal cushion to end the match drawn on three apiece.
Wood opened the scoring in the 11th minute after slipping away from his marker to nod the ball under the body of Birmingham goalkeeper Jack Butland and into the back of the net.
His second came in the 18th minute when he sent a firm shot past Butland from 12 yards out.
Wood, on-loan from Premier League outfit West Bromwich Albion, was unlucky not to clinch a hat-trick, firing wide from eight yards out and then rifling in an angled drive that Butland did well to push away at full stretch.
Millwall manager Kenny Jackett was not impressed by his side’s inability to hold on to their three-goal lead, but was happy with the attack.
“It was very frustrating from a winning position,” Jackett says.
“It is why we are where we are. You can’t give three goals away and expect to get anything on too many occasions, which was a great shame because it covered up some of the best attacking football we have played this season.”
The draw means Millwall are now 19th in the 24-team league, just four points above the relegation places.