Victory would have taken the Robins to within two points of their opponents but despite rallying from 4-1 to make it 4-3 in the second half, Brighton scored three late goals to leave the home side five points from safety.
Brighton were two up at the break through goals from Elisabeth Terland and Pauline Bremer before Megan Connolly pulled one back for Lauren Smith's side with a pinpoint free-kick.
The visitors soon restored their two-goal lead when Terland struck again and looked to be cruising when Tatiana Pinto headed home to make it four.
However, City came roaring back and two goals in three minutes from Brooke Aspin and Amalie Thestrup reduced the deficit to one with 16 minutes left.
The home side sensed the chance for a stunning comeback but it wasn't to be.
Madison Haley got Brighton's fifth in the 89th minute before a penalty from Vicky Losada and a calm finish from Katie Robinson in stoppage time secured an extraordinary win for Mikey Harris' team.
The Seagulls are up to ninth, eight points clear of Bristol City in the solitary relegation spot.
Frenetic defeat leaves Robins' survival hopes hanging by a thread With just one win in their first 14 games, Bristol City were already facing an uphill battle to stay in the top flight.
To do so, it was surely vital to take three points in a home game against the side directly above them.
Not only would a City win have really put the pressure on Brighton, it would also have dragged Everton and West Ham back in as well.
But for all the fight they showed when trailing 2-0 and 4-1, their defending throughout always made it unlikely they could claw their way back.
Terland was left all alone to tap in after a corner was flicked on for Brighton's first and Bremer ran past two Robins' defenders to convert her own rebound for the second.
There was time and space again for Terland to finish the third before Pinto had a simple task of heading in the fourth when the home side switched off from a short corner.
Given they were chasing the game, the final three goals were more understandable but Brighton were still able to cut through them each time with alarming ease.
Bristol City have now conceded 45 goals in the WSL this season and, barring something remarkable, they are facing an immediate return to the Championship.
There may not be many more remarkable things than this game this season but if the Robins can stay up from here, that may be one.
Line-ups Bristol City Women Formation 5-4-1
24Morgan5Aspin6Connolly3Struck2Powell
23Jones16Syme8Rodgers22Evans
13Clark 24Morgan 5Aspin 6Connolly 3Struck 2PowellBooked at 22minsSubstituted forSlocombeat 90+5'minutes 23Jones 16SymeSubstituted forBullat 63'minutes 8RodgersSubstituted forWardat 90+5'minutes 22EvansSubstituted forHaylesat 62'minutes 17ThestrupSubstituted forKendallat 90+12'minutes Substitutes 1Bentley 9Hayles 15Bull 29Ward 30Yanez 36Slocombe 38Pearce 39Kendall Brighton Women Formation 4-2-3-1
16Kullberg5Bergsvand2Thorisdottir8Bremer
6Losada10Olme
22Robinson17Ferreira Pinto7Sarri
32Baggaley 16KullbergSubstituted forLiat 67'minutes 5Bergsvand 2Thorisdottir 8Bremer 6Losada 10Olme 22RobinsonSubstituted forJohnsonat 90+7'minutes 17Ferreira PintoBooked at 90minsSubstituted forDentat 90+7'minutes 7SarriSubstituted forLeeat 75'minutes 11TerlandSubstituted forHaleyat 75'minutes Substitutes 9Lee 21Haley 26Li 28Loeck 39Johnson 40Startup 44McEwan 45Dent Referee: Adewunmi Soneye Attendance: 3,468 Match Stats Live Text Post update