Paul Warne’s Millers replicated their 2-0 league home success over the Iron to clinch their final berth against Shrewsbury Town on May 27 and it was a resounding performance brimful of character and resolve very much in keeping with their efforts under Warne in a stand-out 2017-18.
Wood broke the deadlock with a thumping header moments before the break and a 63th-minute angled strike from Vaulks - who netted in the league triumph over visiting Iron - started the Wembley countdown.
It was Warne who got one over ex-Millers team-mate Nick Daws and now he pits his wits against another former Rotherhan fan-favourite in Paul Hurst for the right to be playing Championship football in 2018-19.
For the Iron, it was a second successive play-off semi-final elimination, with matters compounded by the dismissal of captain Rory McArdle for two bookable offences, with the ex-Bradford City player receiving his marching orders 13 minutes from time.
After an evenly-matched game in North Lincolnshire, the first half was another competitive occasion before the Millers seized the initiative - and a crucial opener - in a power-play spell before the break.
A strong period of pressure in the lead-up to the interval finally told when Wood attacked Vaulks’ trademark long throw and buried a header with the half-time whistle moments later being the precursor to an explosion of joy from home fans.
Earlier, Scunthorpe produced some eye-catching slick passages of passing football at times without overly extending Marek Rodak and it was the Millers who produced the goal threat.
The first development ended with an offside flag nipping any celebrations from Duane Holmes - playing in a more central role to Saturday - in the bud after he netted following Josh Morris’s clever pass.
Rodak then held a low drive from Hakeeb Adelakun as the Iron’s passing game caused a few flutters, but the Millers gradually started to cause problems of their own.
Referee Scott Duncan was unmoved after a clumsy challenge in the box from Ryan Yates on Ryan Williams before the hosts went close to an opener just before the half-hour when Murray Wallace blocked Michael Ihiekwe’s effort in the nick of time after the defender initial attempt was charged down following Joe Newell’s corner.
The Millers assumed the ascendancy and a brilliant one-handed reaction save denied Richie Towell before Joe Mattock’s header flashed inches wide following Vaulks’ quality delivery.
Watson then unconvincingly blocked Matt Palmer’s shot, but was powerless to stop Wood’s meaty header.
The tie was just where the Millers wanted it, but they were given an early scare on the restart when only a heavy touch prevented Holmes from racing clear following Ivan Toney’s assist.
Scunthorpe’s indiscipline soon started to creep in with Toney and Rory McArdle handed cautions, the latter for a hefty challenge on Williams as the night started to look like going against them.
The visitors were soon faced with a mountain to climb when the hosts doubled their tally, with Vaulks seizing upon a loose ball after Josh Emmanuel’s cross was only half-cleared to fire home on the turn - the prelude to Millers fans starting to break into song about Wembley.
A key block by the redoubtable Wood then denied Toney at the other following Morris’s low cross and similar resolute defending from Mattock got in the way of another Toney effort as the visitors desperately sought a way back in.
Wood stayed alert to then deny Toney again after Rodak recklessly hared out of goal before sub Cameron McGeehan wasted a point-blank chance to follow up his goal at Glanford Park, heading wide under pressure from Morris’s centre.
Rodak then raced out of goal to block Holmes’ effort as the Iron produced their most convincing period of pressure over the two legs, albeit when trailing by two goals.
Taylor almost added a third before McArdle exited the stage for a late challenge on Newell, who went close to adding to the Millers account on two occasions.
An impressive reaction save from Rodak thwarted Holmes at the other end with the Millers not to be moved.
Rotherham United: Rodak; Emmanuel, Wood, Ihiekwe (Ajayi 52), Mattock; Vaulks; Williams (Taylor 68), Palmer, Towell, Newell; Smith. Substitutes unused: Price, Forde, Ball, Purrington, Lavery.
Scunthorpe United: Watson; Vermijl, McArdle, Wallace, Townsend; Holmes, Yates (Hopper 83), Ojo, Morris; Adelakun (McGeehan 62), Toney (Novak 80). Substitutes unused: Kelsey, Bishop, Burgess, Sutton.
Referee: S Duncan (Northumberland).
Attendance: 11,061 (1,102 Scunthorpe fans).