John Swift's penalty on the stroke of half-time handed Carlos Corberan's men the lead against the run of play in a crunch top-six meeting.
But Tony Mowbray returned to haunt a club where he remains so revered as the Black Cats climbed above the Baggies and up to sixth.
Cirkin headed in to equalise shortly after the break and stabbed home an excellent late winner six minutes from time after a flowing move reminiscent of Mowbray's promotion-winning Albion 15 years ago.
For Corberan's men the season-defining home fixture at their Hawthorns fortress was one game too many and defeat saw the Baggies down in ninth. They are only two points adrift and still boast a game in hand - Wednesday's trip to Sheffield United - but there is no getting away from a huge opportunity lost at home to a rival leaving a mountain to climb.
Previously their impenetrable home under Corberan, a first Hawthorns defeat in 14 and first since the Spaniard's appointment leaves the Baggies with much work to make anything of fading dreams.
Albion were boosted by significant team news with the return of influential midfielder Okay Yokuslu from a niggling ankle injury.
The Turk had missed four games since picking up the injury late on against Millwall at The Hawthorns but finally passed a fitness test in time for the big clash.
Yokuslu replaced Nathaniel Chalobah, who is the Baggies' latest injury victim with an ankle ligament problem. Taylor Gardner-Hickman, who netted and impressed from the bench at Blackpool, had to make do with a place among the substitutes.
Corberan also welcomed back defender Kyle Bartley from a hamstring problem to take his place on the bench.
Tony Mowbray's injury-ravaged Sunderland were missing as many of 14 players with fitness problems ahead of kick-off. The former Baggies boss made three changes to his starting line-up, with Cirkin, Pierre Ekwah and Abdoullah Ba all introduced from the draw against Huddersfield in midweek.
The visitors saw former Wolves defender Danny Batth, their chief option when it comes to set-pieces, ruled out for the season against the Terriers.
Albion fans and their head coach requested a return of the Liquidator to help crank up the volume levels in what already felt like a Sunday noon melting pot atmosphere.
The noise was deafening in the early stages and the hosts almost took advantage in a pulsating opening few minutes.
Jayson Molumby was heavily involved as ever but couldn't sort his feet while picked out unmarked in the box by a low Jed Wallace cross.
The Irishman then appealed for a penalty after he hit the deck under pressure from Ekwah, but replays suggested the combative Frenchman won the ball.
Home tails were up for 10 minutes as Mowbray's visitors struggled to get a kick. But Corberan had warned the Black Cats like to dominate the ball and the contest soon settled in this pattern.
Nine of the visitors' players were aged 22 or under and that youthful vibrancy was on show. Leeds loan youngster Joe Gelhardt cracked a strike from a corner helped over by Molumby before Alex Palmer raced out bravely to deny dangerman Amad Diallo.
Manchester United loan sensation Diallo, 20, was a real threat and fired narrowly wide from distance after some sloppy play from Yokuslu, who looked off the pace at time.
Albion's midfield was not helped by early yellow cards for Molumby and Yokuslu as busy Sunderland swarmed among them. Palmer was forced into an excellent parried save to his left to deny the tricky Jack Clarke.
Karlan Grant, starting back-to-back league games for the first time in months, showed some intent in darting in from the left flank but his strike from inside the box was closer to the corner flag.
Sunderland had been the sharper and more dangerous side but Corberen's troops edged ahead on the stroke of half-time.
The hosts had been guilty of sitting off and allowing Sunderland play but typical hard pressing from Wallace forced a chance. He charged down a clearance and the ball cannoned to Swift, on the right of the penalty area.
Swift beat Luke O'Nien to the ball and hit the deck. It looked a foul live as referee John Busby eventually pointed to the spot - but replays showed a soft call in which Swift was clever and bought the foul.
Albion's No.19 made no mistake from 12 yards and buried his spot-kick down the middle.
Sunderland could feel hard done to but might have found themselves further behind but for Albion wastefulness and good defending just after the break.
It was pinball wizard in the Black Cats box as Molumby, Grant, Conor Townsend, Darnell Furlong and Swift all had efforts blocked in 10 manic seconds.
Sunderland were anything but wasteful a couple of minutes later.
Away skipper Lynden Gooch was awarded too much room on his side's right and with neither Grant or Townsend able to stop the cross, the American's delivery picked out Cirkin, who drifted in between Molumby, Semi Ajayi and Erik Pieters to plant his header into the top corner.
Palmer saved low from Gooch shortly after but the equaliser rallied the hosts somewhat. The atmosphere cranked up inside The Hawthorns as Albion asked questions of the visiting backline, who stood up tall but were not stretched enough by their hosts. Townsend's header forced a routine save but Patterson was otherwise untested.
The hosts, meanwhile, were fortunate as Palmer's save from distance dropped to Clarke, who somehow fired wide after a five-on-two break.
Yokuslu rattled a volley into the net but the ball was adjudged to already have gone behind. Sunderland were always sharp and saved their best move for the decisive moment. A wonderful, incisive, flowing move from the left eventually teed up Cirkin, whose deflected stab was high beyond Palmer for a crushing blow.
It might have been different. Late sub Gardner-Hickman flashed a fine strike narrowly wide from distance before he dragged an easier effort wide from 20 yards. Academy youngster Mo Faal, another last-gasp change, had his eyes light up on the end of a stoppage time cross. But the 20-year-old fluffed his lines as Albion failed to take their chance.
Albion (4-2-3-1): Palmer; Furlong, Ajayi, Pieters (Bartley, 90), Townsend; Molumby (Faal, 90), Yokuslu (Gardner-Hickman, 85); Wallace, Swift (Rogic, 90), Grant (Albrighton, 83); Thomas-Asante.
Subs not used: Griffiths, Livermore.
Sunderland (3-4-2-1): Patterson; Hume, O'Nien, Cirkin; Gooch (c), Neil, Ekwah (Michut, 68), Clake; Diallo, Ba (Roberts, 68); Gelhardt (Pritchard, 77).
Subs not used: Bass, Taylor, Lihadji, Anderson.
Attendance: 24,764 (1,981 Sunderland fans)
Referee: John Busby