The win strengthens Villa's play-off hopes, but Rotherham remain in the bottom three despite a spirited display.

"I thought we were magnificent second half," Smith said.

"We can talk long and hard about the quality of players we've got but tonight was about spirit."

Tammy Abraham had already missed a penalty for Villa when Mings conceded a spot-kick for handball, but Smith felt the second yellow card shown to the on-loan Bournemouth defender was unnecessary.

"For me there's too much inconsistency in the decision making," he added.

"They started better than we did today. They got in our faces, closed us down, were competitive – sometimes on the wrong side of it for me, I thought some of our players needed more protection.

"Tyrone's getting clipped round the ankles, retaliates and gets a yellow card. Their lad scythes down Jack Grealish for a penalty and doesn't get cautioned.

"Then their lad has a shot, it hits Tyrone on the arm but for me never a yellow card. Why do you give another one? I don't understand it."

The home side started brightly, with Jon Taylor drilling a low effort wide and Semi Ajayi forcing visiting keeper Jed Steer into a smart save.

Madley pointed to the spot after 11 minutes when Grealish was upended by Clark Robertson, but Abraham's weak effort was turned behind by Marek Rodak.

Mings had already been booked when he needlessly handled Joe Newell's cross and was promptly given his marching orders.

Vaulks made no mistake from 12 yards as he blasted the resulting spot-kick past Steer to give the Millers a deserved half-time lead.

However, the game turned on its head within moments of the second half starting.

Madley ruled that Ajayi had deliberately handled Ahmed Elmohamady's cross from the right, and substitute Kodjia fired his penalty into the top corner.

Villa then went ahead in the 51st minute, with Grealish playing an excellent one-two with Elmohamady before placing a calm finish beyond Rodak.

Rotherham manager Paul Warne admitted Mings' sending off had ultimately not worked in his side's favour.

"It was a great spectacle for the neutral," he said.

"I thought it was a bit harsh for a second yellow. The first 10 minutes second half have swung the game and we weren't good enough on the night to get a second goal.

"I take great pride in the first half performance against the form team in the championship.

"I thought we lost a little bit of a battle in the middle of the pitch. Their quality with the ball told with the randomness of it being 11 against 10.

"A point would have been a good point tonight but it wasn't to be unfortunately."

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