All three Fleetwood central defenders scored - Nathan Pond into his own net - and Joe Newell volleyed Rotherham into a short-lived 2-1 lead after the break before centre-back Wood bundled in the 77th-minute winner.
The Millers made changes from the side which lost 3-1 at Charlton. Richie Towell returned from hamstring trouble in midfield and Will Vaulks moved to right-back at Josh Emmanuel’s expense. The Millers also went with two up front, former Fleetwood player David Ball partnering Michael Smith with Ryan Williams dropped to the bench.
Fleetwood named an unchanged side in their bid to make it eight games unbeaten under John Sheridan.
It took Fleetwood just five minutes to take the lead. Ashley Hunter curled in their second corner and central defender Ashley Eastham forced the ball home after his initial downward header had been blocked by Marek Rodak.
Smith headed wide in reply but Rotherham were level in the 12th minute when Joe Newell curled the ball behind the defence and Anthony Forde’s touch was deflected in off the far post by Fleetwood captain Nathan Pond.
The Millers did most of the pressing as Fleetwood sat back but former Rotherham goalkeeper Alex Cairns was largely untroubled before the break.
Rotherham went ahead five minutes after the break when former Millers player Toumani Diagouraga headed out a corner and Matt Palmer laid it into the path of Newell, who volleyed home from the edge of the area.
Fleetwood were soon level. They were awarded a free-kick on the right and Ashley Hunter’s delivery was headed home by unchallenged central defender Cian Bolger from around six yards.
Rotherham were not to be denied and a tumbling Wood converted from Newell’s curling free-kick from the right.
Smith was denied on several occasions and Vaulks headed wide from a corner as Rotherham sought to make the game safe.
Fleetwood almost equalised in the 90th minute as Wes Burns cut in from the left but Rodak made a brave block at his feet.