Rotherham’s hopes of bouncing straight back to the Championship remain alive after they booked their place in the League One play-off final with a 2-0 win over Scunthorpe in the semi-final second leg.

The Millers, relegated from the second tier last year, triumphed 4-2 on aggregate after goals either side of half-time by Richard Wood and Will Vaulks at the New York Stadium.

That sets up the final at Wembley against Shrewsbury on 27 May, with Paul Warne coming up against his former Rotherham team-mate Paul Hurst, the Shrewsbury manager.

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For Scunthorpe, who had Rory McArdle sent off in the second half, it is more play-off heartache as they fall at this stage for the second successive season and they must now decide whether to give the caretaker manager Nick Daws the job or look elsewhere.

Such a routine night for Rotherham did not look on the cards. Scunthorpe were calm in possession and moved the ball well but only had Hakeeb Adelakun’s low effort, which Marek Rodak saved comfortably, to show for their dominance.

Rotherham began to take control and Rory Watson, in for the injured Matt Gilks, made two brilliant saves to keep Scunthorpe level. First he did well to palm away Michael Ihiekwe’s close-range header and then did even better to brilliantly claw out Richie Towell’s curling effort, which looked destined for the top corner.

Watson also kept out a low drive from Matt Palmer but he was beaten in first-half added time. Vaulks launched a long throw into the area and Wood climbed highest to nod into the bottom corner.

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Rotherham were oozing confidence after the restart and put one foot firmly on Wembley Way in the 63rd minute when they went 2-0 up. A flowing move ended up with Josh Emmanuel on the right-hand side and his low cross ended up at the feet of Vaulks, who fired into the bottom corner from eight yards.

Scunthorpe found some life and attempted a comeback. Ivan Toney was denied a goal back by a Joe Mattock block, while Cameron McGeehan missed a golden chance when he somehow headed wide from close range. Rodak then had to be quick off his line to save from Duane Holmes before Scunthorpe’s task became harder when McArdle was dismissed for a second yellow card in the 77th minute.

Still they pressed and Rodak produced a flying save to deny Holmes, his best of the match. Rotherham held firm, seeing out seven minutes of added time to spark exuberant celebrations.