The Clarets led twice through Yana Daniëls and Claudia Walker and showed fantastic resilience to keep fighting until the death, with the result maintaining their place at the top of the league table.
There were two changes from the team’s last Northern Premier Division match against West Bromwich Albion a week ago, with Millie Chandarana making her first league start of the campaign.
Charlie Chadwick came in for Kelly up front, with central midfielder Daniëls wearing the captain’s armband.
It took just three minutes for the skipper to open the scoring. When Walker’s cross was palmed into her path by Feds ‘keeper Liz Hobson, she finished coolly into the bottom left corner.
Play was then stopped with seven minutes on the clock to allow a particular area of the pitch to be cleared of standing water. After a 37-minute delay, the match resumed.
The visitors restarted the better of the two teams and Kirstie Levell was forced into two fine saves in a four-minute spell to keep her team ahead.
After thwarting Chloe Fisher from close range at her near post, the Burnley ‘keeper stood tall to deny Katie Anderson after a neat one-two on the edge of the area.
Their pressure eventually told in the 41st minute as Mia Parry played Anderson through one-on-one, and the winger poked past Levell to equalise.
Burnley fought straight back and restored their lead before half-time after great work from Chadwick. She beat her defender and cut the ball back for Walker, who finished first time from eight yards.
The second half started in battling fashion, with the slick pitch encouraging plenty of slide tackles from two competitive sides.
Chadwick and Ravening both come agonisingly close to extending our lead before the hour but after the former stabbed narrowly wide of a post, the latter couldn’t quite latch onto a Walker cross.
Feds then levelled with a huge stroke of luck in the 73rd minute. After Jess Brady’s shot was saved by Levell, Dee Bradley struck the ball off Emma Siddall and it flew into her own net.
Lou Roberts turned to her bench for the only time seven minutes later, replacing Paul and Walker with Tilly Wilkes and Kelly respectively.
There was a huge penalty shout at each end before the clock hit 90, with Burnley convinced Bradley was bought down in the area following a set piece.
Nothing was given, though, but the fairy-tale ending came in the second minute of stoppage time.
Ravening hooked a long ball forwards which Kelly raced onto and after taking a touch to compose herself, she rifled the ball past Hobson for a deserved winning goal.
The Clarets now have 20 points from their eight league matches to date, ahead of a trip to Stoke City on Sunday 2nd November.
Burnley: Levell, Docherty, Siddall, Matthews, Walker (Kelly 80), Ravening, Bradley, Chandarana, Chadwick, Daniëls, Paul (Wilkes 80)
Unused Substitutes: McAloon, Robinson, Richards, Cairns, Hartley
Liverpool Feds: Hobson, Thompson, Fryer, Fletcher, Fisher (Collins 57), Parry, Smith, Coulthard (Butcher 64), Brady, Anderson, Johnson (Carrington 46)
Unused Substitutes: Pugh-Jones, Cole, Pilgrim
Goals: Daniëls 3’, Anderson 41’, Walker 44’, Siddall OG 73’, Kelly 90+2’