Sunderland's 4-1 win at Derby County lifted them above Burton Albion into 23rd place.
Goals from George Honeyman, Ashley Fletcher, John O'Shea and an Aidan McGeady penalty breathed life into the Black Cats' campaign.
A first win in 11 attempts means they now sit three points adrift of safety, with the Brewers dropping to the foot of the division after their 3-1 defeat to Cardiff City earlier in the day .
Barnsley were denied at the death by Bristol City, with Josh Brownhill netting an injury-time equaliser for Lee Johnson's side in a 2-2 draw at Oakwell.
The former Tyke's 91st-minute effort earned City a share of the spoils after Famara Diedhiou had equalised following Kieffer Moore's early strike.
Brad Potts thought he had earned Barnsley a precious three pints late on, but Jose Morais' side remain in 21st place, four points above Burton and one point above Birmingham City, who play Ipswich Town on Saturday (3pm).
Bolton Wanderers stay six points clear of the relegation zone after they were defeated 2-1 at Leeds United.
Adam Le Fondre pulled one back for 20th-placed Wanderers after Caleb Ekuban and Pablo Hernandez put the hosts in control.
Joining Bolton and Hull City on 39 points are 19th-placed Reading, with Paul Clement winning his first game in charge.
Sone Aluko scored the only goal as the Royals, who had Yann Kermogant sent off late on, beat Queens Park Rangers 1-0.
Cardiff City 3-1 Burton Albion
Hull host Aston Villa on Saturday evening (5:30pm).
Sheffield Wednesday moved 11 points clear of the drop-zone after Atdhe Niuhiu's second double in as many games helped them to beat Preston North End 4-1.
Lucas Joao and Fernando Forestieri also got on the scoresheet, with Louis Moult netting a consolation for the visitors.
Fulham continued their impressive run of form with a 2-0 win at Norwich City, keeping the pressure on Cardiff and Wolves.
Slavisa Jokanovic's side extended their 17-game unbeaten run with Stefan Johansen and Tom Cairney getting on the scoresheet.
They remain in third place, seven points behind Neil Warnock's Cardiff.
Wolves beat Middlesbrough 2-1 despite having Ruben Neves and Matt Doherty sent off in the second-half.
Helder Costa and Ivan Cavaleiro followed up their goalscoring exploits against Burton last time out, putting Wolves two goals up at the break.
Tempers flared with referee Stuart Attwell reducing the visitors to nine men, before Patrick Bamford's injury-time consolation.
That result ensures Wolves stay 13 points clear of third-placed Fulham and six points above Cardiff in second.
Elsewhere, Millwall continued their excellent run of form with a 2-0 win over Nottingham Forest at the Den.
Neil Harris' side scored inside the opening minute for the third time in their last four games as Shaun Williams put the Lions on their way to a win that lifts them up to eighth place.
Fellow play-off chasers Brentford and Sheffield United drew 1-1 at Griffin Park.
