Substitute Bersant Celina was Ipswich's hero as he curled home a sumptuous 90th-minute free-kick with almost his first touch to snatch all three points against Burton.
The Manchester City loanee stepped up and fired home from 25 yards to send the visiting fans delirious at the end of a tight encounter.
Defender Ben Turner gave the home side a deserved lead on 57 minutes after Luke Murphy had been denied by an outstanding save from Ipswich keeper Bartosz Bialkowski.
But Martyn Waghorn levelled with his seventh goal of the season - as many as Albion have managed in total in their 14 Championship games so far - and Celina had the final word.
Albion had the better of the first half largely thanks to a strong wind at their backs, although clear chances to beat Bialkowski were at a premium.
Marvin Sordell, on his return to the side, saw a deflected effort fly wide and from the resulting corner Turner also missed the target. Home skipper Jake Buxton then saw a header from Matty Lund's free-kick find the target but it was an easy save for the Polish keeper.
Connor Ripley, making his Brewers league debut on loan from Middlesbrough, comfortably dealt with an effort from David McGoldrick low to his left but Bialkowski's handling was less assured moments later when he spilled Sordell's shot and had to recover smartly to prevent Lund burying the rebound.
Lund volleyed a first-time effort wide from a sublime pass from Murphy just before the break before McGoldrick and Sordell traded efforts as the first half came to a goalless conclusion.
The second half saw Ipswich look the more purposeful as they looked to take advantage of the blustery conditions at the Pirelli Stadium.
Turner rose highest inside a crowded penalty area to head home a Lund corner just before the hour but the lead lasted less than 10 minutes as former Sunderland and Rangers man Waghorn, from the edge of the box, drilled home through a ruck of bodies into the far corner.
It was Town who looked the more likely to go ahead as Waghorn and McGoldrick both went close, the former seeing a deflected effort just fail to reach Freddie Sears at the back post and McGoldrick sending a curling effort wide from 20 yards.
Still, though, Celina's winner in the final minute was a bitter pill for Albion to swallow in a game where they were more than worth a share of the spoils in their battle against relegation.