Kevin Foley's goal five minutes into the second half had put Wanderers 1-0 up before efforts from Darren Bent and Danny Welbeck put the visitors in the driving seat.
Stephen Hunt drew things level, though, and Ebanks-Blake netted at the death to hand Mick McCarthy's side three much-needed points.
Although they remain in the Premier League relegation zone, 19th-placed Wolves cut the gap between themselves and safety to three points and will take confidence from halting their recent four-match losing run in satisfying style.
Going into the game off the back of four successive defeats, Wanderers had also developed the nasty habit in their last three games of conceding very early goals.
They made a more composed start against Sunderland, though, and were the side to launch the first few attacks.
Ronald Zubar had a cross cleared by Nedum Onuoha after playing a one-two with Foley and the ball skidded away from Matt Jarvis and David Jones as they tried to work something on the edge of the area.
Kevin Doyle then sent a delivery into the six-yard box which was put behind for a corner, but the visitors almost caught Wanderers out soon after as Jordan Henderson fed in Bent, the striker only able to shoot straight at Wayne Hennessey.
Boudewijn Zenden made a better effort with a drive that went wide, but Sunderland were fortunate not to score an own goal when John Mensah connected with Stephen Ward's cross.
The hosts went close again moments later as Craig Gordon flapped at Jarvis' corner, but Richard Stearman was just unable to apply a finish with his head at the far post.
Doyle rifled an attempt too high and Gordon tipped a looping ball from Ward over the bar under the attentions of Jones.
Wolves then had the ball in the net as Stearman stabbed George Elokobi's shot over the line, but the effort was ruled out for offside.
The Black Cats almost took the lead around the half hour mark as Kieran Richardson crashed a free-kick against Hennessey's post.
Wolves were immediately back on the offensive, though, and after good work down the right by Jones and Jarvis, Doyle could not stretch enough to meet the latter's cross.
Zenden found himself in the clear at the other end but failed to control the ball as it dropped for him and Jones headed over from Foley's cross.
Jarvis had the last opportunity of the half, striking into Gordon's arms, before Richardson became the second Sunderland player to be shown a yellow card for a foul on Doyle, following Lee Cattermole into the book.
Wolves began the second half brightly and after Zubar had sent an attempt just the wrong side of the post, they snatched the lead in the 50th minute.
Foley drifted an early ball across to Jarvis, who cut inside and fired an effort at Gordon.
The Scotland goalkeeper could only parry the ball, and Foley was on hand to lash it into the corner.
It was no more than Wanderers deserved on the balance of play, but they had to be alert to ensure they did not let in a swift equaliser, Elokobi blocking a shot from Bent after Henderson's free-kick had caused a scramble in the box.
Cattermole then drilled wide before Sunderland boss Steve Bruce introduced Asamoah Gyan from the bench along with Steed Malbranque, Zenden and Henderson the men to make way.
Doyle was presented with a decent chance when Zubar's deflected shot fell to him, but the Irishman's header was tame and Gordon collected.
Jarvis was next to try to extend his side's advantage, but blazed over from a good position.
The hosts were almost made to pay as a defensive lapse let in Welbeck, but the youngster fired wide.
Within moments of that warning, Sunderland were level as Bent latched onto Gyan's flick-on and coolly slotted the ball past Hennessey.
The hosts looked stung and almost quickly conceded another, Bent just firing wide.
Hennessey then palmed Malbranque's long-range effort away, but Sunderland had real momentum and with just under 15 minutes to go they went ahead, Welbeck heading in Philip Bardsley's cross for his fourth goal in three games.
It seemed as if Wolves had capitulated completely, but to their credit, they pulled themselves back level within four minutes, Elokobi getting a powerful header to Jarvis' cross and Hunt, who had come on for Jones, bundling the ball in.
Suddenly the impetus was with the hosts again and with a minute of the 90 left on the clock, they found a winning goal.
It was another substitute, Ebanks-Blake, who provided it, the former Manchester United striker blasting in after being teed up by Doyle to send Wolves' fans into raptures.