Replacement referee Kevin Wright was immediately thrown into the limelight having replaced the injured Graham Salisbury at half-time at St Andrew's on Sunday, but crucially got two big decisions right.
First Jean Beausejour, who had just rattled the upright from 30 yards, was sent tumbling in the area by Andy King, with Wright pointing to the spot and allowing Marlon King to convert his first league goal of the season.
And within 11 minutes of the restart the game was changed completely when Leicester captain Matt Mills was rightfully shown a straight red card for a two-footed lunge on Morgaro Gomis, despite protests from the visitors.
It was left for Wood to round Kasper Schmeichel late on and add a well-taken and composed second goal to clinch Blues' third successive victory in all competitions.
The game had 0-0 written all over it following an uninspiring first half, with Birmingham boasting the meanest defence in the Football League on home soil and Leicester not having conceded in 412 minutes going into the clash.
Chris Burke was the game's liveliest outlet early on and twice tested Schmeichel, although it was Stephen Caldwell who came within inches of a breakthrough after 13 minutes when his header narrowly landed the wrong side of a post from Beausejour's right-wing free-kick.
The visitors had to wait until just shy of the half-hour mark before their first meaningful effort, Mills stinging the gloves of Boaz Myhill from Lee Peltier's long throw-in.
The second half was delayed by five minutes due to injury sustained by referee Salisbury, with fourth official Wright taking charge of affairs.
And the second period was just 68 seconds old when Beausejour, 30 yards out, took a touch before drilling an unstoppable effort against the angle which had Schmeichel beaten.
Blues had really flown out of the blocks and the Chile international was again at the centre of things just minutes later when he was brought down by Andy King in the penalty area, Marlon King stepping up to slot home the resulting spot-kick.
Matters went from bad to worse for Leicester just six minutes later as Mills was given his marching orders for a two-footed tackle on Gomis near the halfway line.
Schmeichel kept the Foxes in it with two superb saves to deny both Wood and Marlon King when clean through as the clash approached the final 15 minutes.
And the visitors had reasonable appeals for a penalty of their own rejected when Andy King was stopped in his tracks by Liam Ridgewell.
But the game was put out of sight six minutes from time when Keith Fahey fed Marlon King on the halfway line, he turned and instantly sent Wood clear and the New Zealand international rounded Schmeichel to slot home.