Middlesbrough's Brad Jones, left, and Chris Riggott, second left, look on at a header from Wolverhampton Wanderers' Chris Iwelumo, third left, goes wide of the goal
In between, Sam Vokes equalised with a towering header from Dave Edwards' cross.
Southgate was given early cause for concern when Andrew Taylor hurt himself in fouling Matt Jarvis from behind down by the corner flag.
The defender landed awkwardly and looked to have jarred his knee.
He soldiered on for five minutes before limping off to be replaced by Tony McMahon.
From Kyle Reid's resulting free-kick Jason Shackell's glancing header at the near post sailed just wide.
Wolves were not daunted by their Premier League opponents. After all, only three places separated the sides in the football pyramid after Boro's defeat at The Hawthorns eight days ago.
Reid saw a well-struck goalbound shot bravely blocked by Chris Riggott in the seventh minute.
Eventually Boro began to get a foothold in the game and Alves managed to force Wayne Hennessey into action with a shot from just inside the area after cutting in from wide on the left despite the attentions of three Wolves defenders.
A diagonal pass from Alves then set Adam Johnson free on the opposite side but his shot was blocked by Hennessey.
Another Reid free-kick caused confusion inside the Boro penalty box just before the half-hour mark.
Middlesbrough's Afonso Alves celebrates scoring against Wolves
Southgate's side failed to clear their lines as the ball ricocheted about before Neill Collins got the final touch and poked it narrowly wide.
At the other end, Johnson mishit his volley horribly wide after Stuart Downing picked him out with a pin-point right wing cross.
Riggott put his body on the line again after 34 minutes, this time to divert a thunderous Iwelumo effort for a corner.
Boro spurned a golden opportunity to take the lead five minutes before the break.
Downing timed his pass perfectly to beat the offside trap and put Johnson in the clear inside the area.
He took the ball round the advancing Hennessey and looked certain to tap home into an empty net.
But Dave Edwards got back to save the day with a superb goalline clearance.
However, on the stroke of half-time an equally deft pass by Tuncay unlocked Wolves' defence again and, unlike Johnson, Alves was not as wasteful.
The Brazilian coolly dinked the ball over Hennessey and into the far corner for his seventh goal of the season and his fourth in as many matches.
Southgate made his second substitution of the afternoon at the break, replacing Mohamed Shawky with Justin Hoyte.
And it was not be long before his opposite number Mick McCarthy was forced into a change.
Middlesborough's Marvin Emnes scores the winner against Wolves
Chris Iwelumo appeared to suffer an ankle injury on landing after an aerial challenge with David Wheater.
As the Scotland international made his way around the pitch and his replacement Andy Keogh was readied, Vokes' shot got many Wolves fans off their seats. But his right-foot effort from 25-yards was always curling away from goal.
Keogh was introduced after 52 minutes - just after Alves had forced Hennessey to palm away a shot from the right-hand side of the box.
Vokes caused Wolves fans to lift the roof on Molineux when he brought the home side level in the 63rd minute.
The Wales international met Edwards' right-wing cross with a towering header into the bottom corner.
McCarthy stated his intentions by immediately bringing on a third striker - Michael Kightly. Debutant Reid, who signed on loan from West Ham this week, made way.
Boro made their final change in the 71st minute when Emnes replaced Alves.
And after Vokes had missed a glorious chance to win the game for Wolves, Emnes did exactly that for Boro.
Vokes fired wide with the goal at his mercy in the 80th minute after Brad Jones had tipped Keogh's cross into his path. He was immediately replaced by Sylvan Ebanks-Blake.
Wolves fans must have been wishing the former Manchester United trainee was on the field seconds before.
Emnes struck the decisive blow four minutes later.
Matthew Bates tackled Karl Henri deep inside the Wolves half and slipped the ball to Downing.
The England winger set-up Emnes whose low shot found the back of the net via a mixture of Hennessey and the post.