The Cottagers, without an away victory since the opening day of the season and winless in the league at Turf Moor since 1951, appeared to be cruising after goals from Joao Palhinha and Rodrigo Muniz had them 2-0 up inside 21 minutes.
But on-loan Chelsea striker Fofana, on as a substitute just after the hour, got them back into it with a 71st-minute header before bundling in the leveller in the first minute of stoppage time - equalling in 20 minutes his number of league goals for Union Berlin in 17 games during a previous loan this season.
Vincent Kompany's side remain seven points adrift of safety, but this ended a run of 19 Premier League games in which Burnley had lost after conceding first, and the mood inside Turf Moor improved dramatically after Fofana's late intervention.
Kompany's side, whose last league win was away to Fulham on December 23, began well and kept the Cottagers inside their own half. After Lyle Foster dispossessed Tosin Adarabioyo it took a superb recovery tackle from Tim Ream to deny Wilson Odobert a clear shot at goal.
But it fell apart very quickly. Kompany gave a debut to Lorenz Assignon, who arrived on loan from Rennes on deadline day, but the right-back needlessly conceded a 17th-minute corner when he shepherded the ball out of play rather than hook it clear.
The mistake was instantly punished as Andreas Pereira whipped the ball in and Palhinha turned it goalwards, with his header beating James Trafford with the help of a deflection off Sander Berge.
It got worse four minutes later when Antonee Robinson's long punt up field turned into the perfect ball for Muniz to score his first Premier League goal.
The 22-year-old Brazilian, starting in place of the injured Raul Jimenez with new boy Armando Broja on the bench, was played onside by Vitinho as he got goalside of Hjalmar Ekdal, running at Trafford before lifting the ball over the exposed goalkeeper to a chorus of boos from the Turf Moor crowd.
Ekdal was hooked at half-time as Maxime Esteve, Burnley's other deadline day signing on loan from Montpellier, came on for his debut.
Josh Brownhill, making his 100th Premier League appearance, had a shot which picked up a deflection on its way to Bernd Leno, but it was Fulham who continued to probe to the frustration of the home fans.
Willian's curling low shot was pushed aside by Trafford, who then repelled Adarabioyo's powerful header from the resulting corner. Soon after, the goalkeeper made a smart save to deny Muniz at his near post.
Fofana came on for his home debut alongside Johann Berg Gudmundsson just after the hour, and soon set up Brownhill, who blazed wastefully over.
Moments later, the Ivorian was celebrating his first Burnley goal. Assignon led a breakaway down the left, and sent in a cross which sailed over Leno to leave Fofana to head into an open goal.
Marco Silva responded by giving Broja his debut but his decision to reinforce the defence with Kenny Tete backfired.
The Dutchman missed what looked a routine interception of Gudmundsson's ball forward and it ran through to Odobert to send in a low cross, and Fofana beat Ream to the the near post to divert it home.
The goal survived a VAR check for handball, to the delight of the home crowd and the relief of Kompany.