Jimmy Floyd Hasselbaink's side headed to the Victoria Ground having suffered back-to-back defeats for the first time since the Dutchman took over last November.
The hosts looked to have done enough to secure an impressive point, but Hasselbaink's men snatched victory in the 90th minute courtesy of substitute Florent Cuvelier's low strike.
Defeat is a body blow to Hartlepool's increasingly slim survival hopes, with Ronnie Moore's men now eight points adrift of safety at the bottom of the table. Burton, meanwhile, moved back to the league's summit, sitting two points ahead of Shrewsbury Town, who rued a 95th-minute Sullay Kaikai equaliser in their 1-1 draw at home to Cambridge United.
Elsewhere at the top, an Alfie Mawson strike five minutes from time rescued a 2-2 draw for Wycombe Wanderers at Southend United, while a late own goal from Luke Wilkinson sealed a 3-2 win for 10-man Morecambe at Luton Town – their first league defeat at home since September.
Oxford United substitute Callum O'Dowda sealed a 1-0 win over 10-man Bury with an 85th-minute strike, while play-off rivals Plymouth Argyle eased to a 2-0 victory at home to Northampton Town.
John Sheridan's side sit in seventh, level on points with Stevenage, who secured a 2-1 victory at home to Newport County.
It was a bad day for the league's bottom five, who could only manage one point between them, courtesy of Cheltenham Town's 1-1 draw with Mansfield Town that dumped Tranmere Rovers, who went down 3-2 to Dagenham and Redbridge, into the bottom two.
Carlisle United were beaten 3-1 at home to Exeter City, York City lost 2-1 at AFC Wimbledon and Accrington Stanley were held to 1-1 draw with Portsmouth in the day's only other game.
