It arrived seven minutes from time when a replay, which Wolves definitely didn't want, was looking likely. Matthew Bates won a crucial tackle in midfield, Stuart Downing played Emnes through and the finish in off the far post broke Wolves' hearts.
For a £3.2 million signing who has yet to start a Premier League game, Emnes will have to do more than this to prove his worth. But if his winner provides Middlesbrough with the lift they need to preserve their top-flight status it will have proved money well spent.
'A lot of people would have expected us to get turned over here but the players responded well,' said Southgate who has not celebrated a win in the league for ten games. The downside was a booking for Gary O'Neil which will keep him out of this week's game with Chelsea and injuries to Andrew Taylor, Afonso Alves and Mohamed Shawky.
His team selection showed Southgate has no margin for error – only regular goalkeeper Ross Turnbull was allowed the day off. In contrast Wolves put leading scorer Sylvan Ebanks-Blake and the dynamic Michael Kightly on the bench. The Championship leaders go to Reading on Tuesday and you could understand Mick McCarthy's thinking.
Wolves sensed their chance to declare equality with the Premier League strugglers and attacked with bite and brio at the start, an early free-kick producing a header from Jason Shackell which almost found the far corner.
Kyle Reid's change of pace was a torment for the visitors in the early stages and Middlesbrough were grateful for David Wheater's ability to put himself in the right position at the right time. Gradually they settled and began to show they could make good used of the ball. Adam Johnson had three decent chances to score over the 90 minutes, the second of which saw Dave Edwards clear heroically off the line after the winger had rounded Wayne Hennessey.
Tuncay's creativity was seen at its best in the 43rd minute as he played Alves into space inside the area. The finish from the Brazilian was sublime, a deft flick over Hennessey and Boro had the lead.
It might have been doubled as Downing continued to shine in a team now demonstrating self-belief. At the start of the second half Alves extended Hennessey soon after Sam Vokes had sent a fierce attempt whistling narrowly wide. Vokes then brought Wolves back into the picture with a towering header at the far post but even though Ebanks-Blake and Kightly joined the fray they couldn't find a second equaliser.
Middlesbrough's pursuit of Crystal Palace's Ben Watson has ended in failure with Southgate saying the midfielder is likely to join Wigan.
Wolverhampton: Hennessey, Edwards, Shackell, Collins, Hill, Jarvis (Ebanks-Blake 81), Henry, David Jones, Reid (Kightly 65), Iwelumo (Keogh 52), Vokes.Subs: Craddock, Friend, Ikeme, Foley. Booked: David Jones. Goals: Vokes 63. Middlesbrough: Jones, Bates, Wheater, Riggott, Taylor (McMahon 7), O'Neil, Sanli, Shawky (Hoyte 46), Adam Johnson, Downing, Alves (Emnes 70).Subs: Porritt, Bennett, Turnbull, Craddock. Booked: O'Neil.Goals: Alves 44, Emnes 83.Referee: Rob Styles (Hampshire).