Guro Bergsvand bundled the ball into her own net after Everton winger Aurora Galli had taken advantage of a mix-up at the back.
In a tightly-matched game where neither goalkeeper came under too much pressure, the first goal did not arrive until the hour mark.
Everton went ahead when twins Karen and Sara Holmgaard combined, with substitute Karen nodding a cross past Sophie Baggaley at the back post.
But the Toffees were not able to celebrate their lead for long as Brighton levelled just two minutes later.
Tatiana Pinto smashed home a rebound after Maisie Symonds hit the crossbar with a free-kick and Everton keeper Courtney Brosnan failed to clear the rebound.
Brosnan had earlier made a crucial first-half save to prevent a scuffed Elisabeth Terland shot trickling into the Everton net.
Terland has 12 goals in the league this season but never really found her footing on Friday night as she was starved of service.
Both teams mostly cancelled each other out in the middle of the park and were limited to half-chances - and it was a defensive error which gave Everton the chance to snatch the win.
While avoiding the drop has seemed a formality for some time, Everton and Brighton will both be mathematically safe by the end of the weekend unless bottom-placed side Bristol City pick up points against Liverpool on Saturday (12:30 BST).
Line-ups Brighton Women Formation 4-3-3
26Li5Bergsvand14Carabali3Pattinson
18Symonds17Ferreira Pinto10Olme
22Robinson11Terland7Sarri
32Baggaley 26LiSubstituted forLeeat 66'minutes 5Bergsvand 14CarabaliSubstituted forThorisdottirat 84'minutes 3Pattinson 18SymondsSubstituted forHaleyat 65'minutes 17Ferreira PintoBooked at 59minsSubstituted forKullbergat 84'minutes 10Olme 22Robinson 11Terland 7SarriSubstituted forBremerat 55'minutes Substitutes 2Thorisdottir 8Bremer 9Lee 16Kullberg 20Stefanovic 21Haley 28Loeck 44McEwan 45Dent Everton Women Formation 5-4-1
17Hope8Vanhaevermaet20Finnigan27Stenevik23Holmgaard
22Galli21Kuhl7Wheeler10Bennison
1Brosnan 17HopeSubstituted forBissellat 73'minutes 8Vanhaevermaet 20FinniganBooked at 75mins 27StenevikBooked at 49minsSubstituted forDaleat 88'minutes 23HolmgaardSubstituted forVejeat 73'minutes 22Galli 21KuhlSubstituted forPiemonteat 88'minutes 7Wheeler 10BennisonSubstituted forHolmgaardat 55'minutes 25Snoeijs Substitutes 2Veje 11Bissell 13Hart 15Dale 18Piemonte 28Holmgaard 30Wilding 47Olesen Referee: Kirsty Dowle Attendance: 4,987 Match Stats Live Text Post update