LAST-GASP Chris Brunt came to the rescue with a 93rd-minute leveller to bag some reward on a night of pure frustration for Albion.
The Baggies created numerous chances and bossed the Portman Road clash for long spells.
But they fell behind against the run of play on 68 when referee Stuart Attwell awarded the Tractor Boys the most dubious of penalties.
Not a single Ipswich player appealed when Jonas Olsson beat Damien Delaney to a header just inside the Baggies box.
But Attwell pointed to the spot - and Town skipper Grant Leadbitter tucked it away.
To their immense credit, Roberto Di Matteo's men kept plugging away but their luck appeared to be well and truly out until Brunt stabbed home his seventh of the season from close range with virtually the last kick of the game.
Albion's failure to score before this point was down to a mixture of poor finishing - with Roman Bednar the chief culprit - and Ipswich centre-halves Gareth McAuley and Delaney producing a terrific rearguard action.
Di Matteo named an unchanged side for the third successive game.
Albion dominated the opening 25 minutes and their first effort on goal came in the fifth minute when Jerome Thomas cut inside from the left and drilled a 20-yard strike just over the bar.
Five minutes later, Olsson flicked on Graham Dorrans' left-wing corner and Bednar missed a glorious chance to open the scoring as he volleyed over from inside the six-yard box.
The Albion pressure continued when Brunt curled a delicious ball into the path of Bednar on the right-hand side of the box.
The Czech striker got his shot away which keeper Arran Lee-Barrett could only parry but McAuley cleared in the nick of time to deny Robert Koren any chance from the rebound.
More slick Baggies passing on 18 saw Dorrans find Koren inside and the Slovenia captain teed up Brunt, who fired straight at Lee-Barrett from 20 yards.
Lee-Barrett was lucky to stay on the pitch in the 21st minute when he chopped down Bednar just outside the area as the Baggies hitman raced onto Brunt's pinpoint pass and beat the Town keeper to the ball. Referee Attwell only showed Lee-Barrett a yellow card as there were covering defenders.
Two minutes later, the Tractor Boys threatened for the first time when Jon Stead swept in a cross from the right and David Norris nicked the ball in front of Olsson before firing a low shot just past the far post.
Seconds later, Koren's right-wing centre was met by Bednar, whose downward header was saved low down by Lee-Barrett.
Dorrans threaded a delightful ball through to Jara in the 26th minute and the Chilean international cut it back for Koren who looked certain to score, only for his goalbound effort from ten yards to get blocked by McAuley's last-gasp lunge.
Scott Carson needed to be at his best in the 33rd minute as he stooped low to his left to turn Norris' low drive around the post after the Ipswich midfielder had been set up by Pablo Counago.
From the resulting Leadbitter corner, the unmarked McAuley headed wide when he should at least have hit the target.
Four minutes before the break, a loose ball dropped for Stead on the edge of the box but he screwed his half-volley wide of goal.
Back came Albion and when Bednar challenged Lee-Barrett for Dorrans' cross in the 42nd minute, the Town custodian could only half-punch clear.
Brunt lobbed the loose ball goalwards, only to see that man McAuley clear off the goalline.
Moments later, Jara teed up Dorrans and the Scotland international flashed a 20-yard strike just past the right-hand angle of post and bar, with Lee-Barrett beaten.
Ipswich, who were much-improved during the latter stages of the half, could have gone into the break in front when Jaime Peters exchanged a one-two with Counago and raced clear.
But the Canadian winger saw his shot from just inside the area blocked by the towering Carson.
Three minutes after the break, Delaney headed Counago's left-wing corner goalwards and Marek Cech's unwitting back header made life difficult for Carson, but the Baggies skipper was alert and gathered on the goalline.
Normal service soon resumed with Albion back on the attack.
And only David Wright's last-gasp lunge at the far post denied Brunt a tap-in after Bednar had flicked on Thomas' left-wing cross.
Lee-Barrett almost shot Ipswich in the foot on 54 when he threw the ball straight to Thomas, whose attempted shot rebounded to Cech.
The Slovakia defender crossed for the unmarked Bednar who flashed a header past Lee-Barrett and inches the wrong side of the far post.
But disaster struck in the 68th minute when referee Attwell awarded Ipswich the softest of penalties, pointing to the spot for Olsson's innocuous challenge on Delaney from a long throw-in.
The giant Swede was booked for his troubles and Leadbitter stepped up to fire his team in front from 12 yards.
Di Matteo threw caution to the wind by bringing on Ishmael Miller for Koren and, shortly after, Filipe Teixeira for Thomas.
Despite their 'ref justice', Albion refused to lie down and another chance came their way 12 minutes from time when Dorrans' 78th-minute shot was blocked and fell to Miller - but he fired weakly at Lee-Barrett in a crowded penalty area.
With Albion piling men forward, they were susceptible to the counter-attack and the game could have been beyond them on 85 when Tamas Priskin cut inside Gabriel Tamas.
The impressive Carson again came to the rescue, denying the Town sub with a fine block, and Leadbitter planted an awkward header wide of the gaping net from the rebound.
That slice of luck was no less than Albion deserved and they finally got their just desserts three minutes into stoppage time.
Sub Simon Cox's shot was blocked in front of goal and Brunt was on hand to prod home the rebound.
IPSWICH (4-4-2): Lee-Barrett; Rosenior, McAuley, Delaney, D Wright (Balkenstein 72); Peters, Leadbitter, Norris, Colback; Counago (Edwards 65), Stead (Priskin 79). Subs not used: McLoughlin (gk), Garvan, Martin, John.
ALBION (4-5-1): Carson; Jara, Tamas, Olsson, Cech; Brunt, Koren (Miller 68), Mulumbu (Cox 80), Dorrans, Thomas (Teixeira 76); Bednar. Subs not used: Kiely (gk), Mattock, Zuiverloon, Martis.
GOALS: IPSWICH - Leadbitter (pen 68). ALBION - (Brunt 90+3).
BOOKINGS: IPSWICH - Lee-Barrett (foul 21), Leadbitter (unsporting behaviour45+2). ALBION - Mulumbu (foul 35), Dorrans (unsporting behaviour 45+2), Olsson (foul 66).
REFEREE: S Attwell (Warwickshire).
ALBION STARMAN: Marek Cech.