The Bianconeri earned a 2-1 comeback victory at the Dacia Arena to move up to 15th and within three points of opponents Cagliari, who were defeated 2-1 by Lazio on the same day.
Juventus would have been crowned champions of Italy for a ninth successive year had they picked up victory against Udinese in Thursday's clash.
Fofana's goal arrived in added time and it could prove to be a huge strike for Udinese in their battle to avoid the drop.
Luca Gotti's side entered the match on a poor run that had seen them collect one point from the last nine on offer and were just four points above the bottom three at kickoff.
As it is, however, they are now within one win of making certain of their top-flight status.
Realistically, they can probably lose all three remaining games and stay up given that 18th-placed Lecce have a seven-point deficit to make up.
Indeed, victory at the Sardegna Arena this weekend in their 50th Serie A meeting with Cagliari and they will be level on points with their opponents in 13th.
Cagliari have dropped off massively since winning back-to-back games against SPAL and Torino late last month, failing to win any of their seven matches since then.
Four of those games have finished all square - only Hellas Verona have drawn more in the Italian top flight this term - including their last two at home.
In fact, the Islanders have won only won of their last nine home games, whereas Udinese have won two of their last three away, as many as they managed in their previous 14.
After throwing away a one-goal lead to lose against Lazio last time out, Walter Zenga's men could do with stopping the rot ahead of games with Juventus and AC Milan to conclude the season.
Cagliari's Serie A form: LDDLDL
Udinese's Serie A form: DWLDLW
Artur Ionita returned from suspension to start against Lazio last time out and is likely to retain his place in central midfield on Sunday.
There will be no Radja Nainggolan for Cagliari, however, with the midfielder being ruled out for the season with a calf injury.
Striker Joao Pedro has scored four goals against Udinese during his career, although only one of those has come at home.
Udinese have a few players on the sidelines, but they did at least welcome Stefano Okaka back from suspension for the win over Juventus.
Fofana, the late matchwinner in midweek, has scored two goals against Cagliari in Serie A, including in his most recent game against them back in December.
Cagliari possible starting lineup:
Cragno; Walukiewicz, Klavan, Lykogiannis; Farago, Nandez, Ionita, Rog, Mattiello; Pedro, Simeone
Udinese possible starting lineup:
Musso; Becao, Troost-Ekong, Nuytinck; Avest, Fofana, De Paul, Sema, Zeegelaar; Nestorovski, Okaka
We say: Cagliari 1-2 Udinese
Udinese are surely now safe from the drop after beating champions-elect Juventus and this is a fixture that they tend to do well in. The visitors have won three in a row against Cagliari and, given the form of Zenga's side, we are backing an away win on Sunday.