Manager David Martindale admits Livingston's Scottish Premiership survival hopes are "very slim" after they beat Ross County.
Bruce Anderson lobbed bottom side Livi in front after a mistake by County's Ryan Leak and Sean Kelly's second-half penalty ensured the gap between the sides was reduced to nine points with four games to go.
The result means the visitors were unable to draw level with or overtake St Johnstone, who lost at home to Hibernian.
The team finishing bottom go down automatically and the second bottom side meet a Championship team in the two-legged Premiership play-off final.
Aberdeen and Motherwell are not yet arithmetically safe from the relegation play-off spot but well placed with gaps of eight and seven points, respectively.
"As long as I'm at this club, we'll never not fight," said Martindale. "I know the probability of staying in the Premiership is very slim but it's not going to change by motivation, my passion, my emotions coming into work."
Martindale could not have put it more plainly prior to kick-off - saying, "we need to win" - and his players responded with the opening goal.
Stephen Kelly's long ball should have been mopped up by Leak but his tame header back to Ross Laidlaw was short and Anderson pounced, lifting the ball over the stranded goalkeeper.
A similar scenario almost took place at the other end as defender Ayo Obileye's header bounced into Josh Sims' path but keeper Shamal George blocked the shot.
Anderson had headed wide before his goal and Daniel Mackay's shot on the turn was held by Laidlaw in what was a strong first-half showing that continued into the second period.
Mackay's attempted pass in the box struck the hand of Michee Efete and Kelly confidently converted the resulting spot-kick.
A penalty appeal by Anderson following Efete's challenge in the first half had been given short shrift by referee Willie Collum and it was a similar tale as Mackay came together with Josh Reid in Livi's box.
George then saved an Eamonn Brophy header with the help of Sean Kelly's chest, not his hand as claimed by the visitors.
And a late free-kick effort by Yan Dhanda and long-range shot by Brophy were dealt with by George as the intrigue of the relegation battle extended into next weekend's fixtures.
Player of the match - Shamal George (Livingston)
Livi still clinging on - analysis
Livingston's top-flight status remains under severe threat but this performance was much more reminiscent of the side that was promoted in 2018 and proceeded to hold their own under Gary Holt and Martindale.
Their defence was resolute, their forwards a nuisance to the opposition, and their overall battling qualities ensured just a fourth league victory of the campaign.
In contrast, County looked very unlike the team that beat Rangers for the first time in their history just 13 days previously. Gone was the attacking intent and determination that served them so well that day.
The silver lining for interim boss Don Cowie is that St Johnstone, the most likely rival in the race to avoid the play-off place, also lost.
What the managers said
Livingston manager David Martindale: "To a man, the players did themselves proud. The back four defended the box incredibly well. That was the difference."
Ross County interim manager Don Cowie: "Credit to Livingston, I thought they played really well. We got a lot of plaudits for the performance against Rangers and the criticism we get on the back of this performance we deserve as well.
"We gifted them their first goal. We had a few moments here there but, over the piece, we can have few complaints and Livingston thoroughly deserved to win."
What's next?
Ross County host Hibernian next Saturday, while Livingston are away to Motherwell with both games at 15:00 BST.