Wood, 19, signed on loan from West Brom in the summer, took his tally to four in two matches with a close-range finish in the 29th minute, a clinical strike from outside the penalty area midway through the second half and a late header.
Millwall, nudged down into 14th place by the Blues' big climb, were not without their own chances, especially in the first period, but Wood's first goal settled Blues and his second proved decisive for Chris Hughton's side, who secured their second straight home league win.
Wood completed a memorable day for Blues fans by rounding off the scoring in the final minute.
Hughton made two changes to the side that drew with Watford in their last league game, with defender Steven Caldwell and midfielder Morgaro Gomis returning.
Millwall handed a debut to winger Liam Feeney, a deadline-day signing from Bournemouth, while striker Jay Simpson made his first start following his arrival from Hull for a second loan spell.
Defender Tony Craig and midfielder Liam Trotter also returned to the side.
City striker Wood forced Millwall goalkeeper David Forde to save his 20-yard shot inside the first 10 seconds and Blues keeper Boaz Myhill then pushed away Hamer Bouazza's free-kick in a lively opening.
Bouazza dragged another angled effort wide and Lions striker Darius Henderson headed over Feeney's inswinging corner.
Millwall threatened again as Feeney's 20-yard effort was punched away by Myhill and Trotter fired a long-range shot over the crossbar.
But it was Blues who broke the deadlock. Jean Beausejour slipped the ball inside from the left edge of the penalty area and Wood converted from close range.
Curtis Davies went close to extending the Blues' lead, but headed Beausejour's corner off target as half-time approached.
Millwall's new boy Simpson was then denied an equaliser when his snap-shot from several yards out in the 43rd minute was brilliantly saved by Myhill.
Simpson, voted player of the year at The Den during his previous spell during the 2007/8 season, stung Myhill's hands with another effort soon after the restart, but the home side looked increasingly comfortable in possession.
The Blues' killer goal arrived in the 62nd minute and Wood this time showed his potency from outside the area, collecting Adam Rooney's square pass and arrowing a shot into Forde's bottom right-hand corner.
Moments before Wood struck his second Millwall manager Kenny Jackett sent on James Henry and Dany N'Guessan for Bouazza and Feeney, but it was Blues who continued to prosper.
Beausejour swung over another corner in the 68th minute and Davies was again left free to direct his header goalwards, this time seeing his effort come back off the crossbar.
Millwall by this time had been restricted to Simpson's speculative shot from outside the area and although Trotter forced Myhill into another fine save in the closing stages it was too little too late for the Londoners, who conceded a late third when Wood headed home Chris Burke's right-wing cross and slipped to their second league defeat of the season.
Source: DSG