Wood, who netted in the play-off semi-final second leg over Scunthorpe, truly surpassed himself by scoring twice from set-piece deliveries from Joe Newell, with his second on 103 minutes securing promotion - after Alex Rodman’s 58th-minute strike cancelled out Wood’s 33rd-minute opener.
It resulted in ecstatic scenes with the Millers, who missed an early penalty through David Ball, producing a fairytale end to a compelling season in extra time.
Millers chief Warne sprang a surprise by fielding Ball from the start, but his first contribution was a distinctly flat one.
Assuming penalty responsibilities after Beckles pulled the shirt of Wood in the box, Ball was denied by the prowess of Henderson, with the keeper, widely recognised as the stand-out custodian in League One this term, guessing correctly by diving to his right to keep out the spot-kick on nine minutes.
To his credit, Ball dusted himself down impeccably and was at the heart of a strong half and spirited response from United, which was rightfully crowned by an opener.
Wood got the run on Beckles - lucky not to concede a second penalty after tangling with the Millers skipper - following another quality corner delivery from Newell before emphatically planting a downward header past Henderson following Newell’s deadly centre.
It was no more than the Millers, who settled and imposed themselves on proceedings far quicker than the Shrews, deserved.
The incision and conviction all arrived from those in red with the Shrews failing to show up in a meek first-half showing.
Marek Rodak was protected well with the Millers going close to a second before the btreak when Richie Towell’s half-volley flew over.
It was a half dominated by the Millers, but the narrative changed on the restart, with Shrewsbury - no doubt cajoled by some interval words from Hurst - stepping things up and levelling on 58 minutes.
A super-slick free-kick routine caught out United, with Shaun Whalley playing the ball short to Matt Sadler, whose clever flick was converted from close range by Rodman.
The Millers regrouped and spurned a huge chance to retake the lead on 74 minutes when substitute Caolan Lavery, sent clear by Will Vaulks, agonisingly steered his effort wide of a gaping goal.
Chances arrived at both ends towards the end of normal time, with the pick of them seeing Henderson making a brilliant reaction save to deny substitute Ryan Williams in injury-time.
The scene was set for a hero in extra time and Wood came up trumps, stabbing in Newell’s delivery.
Rotherham United: Rodak; Emmanuel, Wood, Ajayi, Mattock; Taylor (Williams 75) Vaulks, Towell, Newell (Forde 110); Ball (Lavery 71); Smith. Substitutes unused: Price, Palmer, Purrington, Cummings.
Shrewsbury Town: Henderson; Bolton (Riley 73), Nsiala, Sadler, Beckles; Godfrey; Whalley, B Morris (Payne 56), Nolan, Rodman; C Morris (John-Lewis 65). Substitutes unused: MacGillivray, Lowe, Brown, Jones.
Referee: R Jones (Merseyside).