An early goal by Aden Flint and a brace from Famara Diedhiou put sixth-placed Bristol City 3-0 up within 37 minutes
But two own goals - including one from Marlon Pack deep into stoppage time - and a strike by Aiden McGeady earned the Black Cats an unexpected point, which kept them one off the bottom and within three points of safety.
Wolverhampton Wanderers moved 13 points clear at the top after beating Queens Park Rangers 2-1 at Molineux. Alfred N'Diaye and Helder Costa put the runaway leaders 2-0 up with three-quarters of the game still to go.
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Conor Washington pulled one back soon after halftime, but the Londoners were unable to find an equaliser.
The win extended Wolves' lead as Derby County, their nearest rivals, were held to a 1-1 draw at home by Norwich City.
Matej Vydra's 17th league goal of the season was cancelled out by James Maddison's second-half penalty - his ninth goal of the campaign for Norwich.
Fulham failed to close the gap when Adam Le Fondre's equaliser earned Bolton Wanderers a share of the points in a 1-1 draw at the Macron Stadium after Matt Targett had given fifth-placed Fulham an early lead.
Sheffield United and Middlesbrough remained hot on the heels of those sides in the playoff places after 2-1 home victories over Leeds United and Reading respectively, but Preston North End faltered, being held 1-1 by Brentford.
Barnsley drew 1-1 with Sheffield Wednesday in the South Yorkshire derby, but Hull City's 2-0 victory at Nottingham Forest sent Barnsley into the bottom three.
Burton Albion remained bottom after a goalless draw at Ipswich Town.
(Reporting by Neville Dalton, editing by Ed Osmond)
