Grateful for small mercies, Gareth Southgate has another platform on which to attempt the recovery his team and managerial reputation desperately need. Marvin Emnes, signed for £3 million from Sparta Rotterdam last summer and used only once in Middlesbrough's starting line-up, finished sharply seven minutes from time to secure a fifth-round place by no means everyone would have expected of them in their current state.
The Dutchman came on as a substitute and bailed out his under-pressure manager by cannoning a powerful low left-foot shot in off the far post from Stewart Downing's pass. Only seconds earlier, Matt Jarvis had sidefooted wide from 12 yards when Andy Keogh's cross was diverted to him – such are the Cup's fine margins.
Middlesbrough's need for a win after 10 League games without one was underlined by their deployment of their best available outfield players.
"A few people would have expected us to be turned over here," said Southgate, who learned before kick-off he had lost out to Wigan Athletic in the £2m chase of Ben Watson. "It was a big ask because we had a young side who became younger still with the injuries we picked up. But we have responded well in this type of fixture in recent years."
Mick McCarthy's selection reflected his desire to hold something back for Tuesday's game at Reading and his re-jigged defence soon looked vulnerable after Jason Shackell and Neill Collins went close from free-kicks by the debutant Kyel Reid.
Adam Johnson, wayward with one ambitious angled volley, should have scored when Downing's through-ball took out a square back line and left him to go round Wayne Hennessey, only for David Edwards to stretch and clear superbly off the line.
Wolves were caught dreadfully square again in the 44th minute and this time they were punished. Tuncay Sanli cleverly fed Afonso Alves, who finished exquisitely with a chip over Hennessey's spread body.
Alves was denied by a brilliant save before Wolves equalised out of nothing just past the hour, Sam Vokes climbing above Chris Riggott to head Edwards' towering right-wing centre into Brad Jones' bottom-right corner.
Maybe Wolves were aware that Middlesbrough's conquerors in each of the past four seasons had gone on to lose in the final but they were thinking of Reading rather than dreaming of Wembley. "If I had a smile at the end, it was because I'd heard Birmingham had lost," McCarthy said.
Referee: Rob Styles
Man of the match: Downing