Dean Smith's side will now face either Leeds United or Derby County at Wembley for a place in the Premier League.
The final is at Wembley Stadium on May 27.
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Jedinak came on with just seconds remaining in the match and - after Jed Steer put Villa in control with great saves from Mason Holgate and Ahmed Hegazi - slotted his side's second spot-kick easily. Their second leg is on Wednesday (Thursday NZ time), with Leeds protecting a 1-0 lead at their Elland Road home.
"The day we knew we were in the play-offs we started working on penalties", the boyhood Villa fan, who...
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"All of us are very hungry and have good legs in us".
With no away goal applicable, extra time reined in as Johnstone parried a low shot 110 minutes in from Jack Grealish. Steer was the hero though, saving penalties from Mason Holgate and Ahmed Hegazi, as Tammy Abraham scored the winning penalty.
Jedinak came on with just seconds remaining and slotted the team's second spot kick as the Villans seek a return to the Premier League after an absence of three years.
Les soeurs Williams se retrouvent à Rome... 21 ans plus tard!
Elise Mertens peut nourrir des regrets après sa 4e défaite dès son entrée en lice en cinq tournois joués sur terre battue cette saison. " C'est fou .