The 21-year-old came off the bench at Turf Moor with the Clarets 2-0 down to earn Vincent Kompany's men a precious point.
It was his second appearance since joining on loan from the Blues last month after his short spell in Germany at Union Berlin was cut short.
And he has quickly made his presence known, with the three-cap Ivory Coast international already proving to be a huge hit with the Burnley faithful.
His opening goal against the Cottagers in the 71st minute was gifted to him with Bernd Leno in no man's land, allowing the forward to head home into an empty.
He then showed a great striker's instinct in the first minute of stoppage time to get on the end of Wilson Odobert's low cross to divert into the back of the net.
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It was the exactly the sort of run - and finish - that Chelsea have been missing this season, with Mauricio Pochettino's side struggling in front of goal.
And the Blues faithful quickly took to social media where they all said the same thing in reference to Fofana's double.
Taking to X, one user said: "Why did we loan out Datro Fofana."
Another messaged: "David Datro Fofana already has two goals on his debut for Burnley today while Chelsea are struggling in front of goal without a proper 9.... I'm tired man."
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A third added: "Why is our best striker on loan at Burnley. We're in the mud."
And one supporter messaged: "Recall Datro Fofana he's our best striker at the club."
This supporter posted: "How Datro Fofana never really got a chance at Chelsea still baffles me."
Meanwhile another stated: "We were in need of a striker and decided to loan out David Datro Fofana."
Fofana's double follows on from the assist he got at the Etihad midweek in Burnley's 3-1 defeat to Manchester City.