The Iran winger ended his long wait for a first Brighton goal against Bournemouth on Saturday, celebrating with joyful tears, and his second quickly followed in a stylish start to 2020.
Chelsea looked to be easing towards a third straight Premier League away win after Cesar Azpilicueta's early strike, failing to add to their lead but largely comfortable at the other end.
However, Jahanbakhsh leapt into an outstanding volley with six minutes of normal time remaining, and Frank Lampard's fourth-placed side were clinging on by full-time.
Chelsea had made a confident start - in stark contrast to the awful early display in Sunday's smash-and-grab at Arsenal - and soon led through their captain.
Tammy Abraham's low shot on the turn following a corner was blocked by Aaron Mooy in front of the goal line, but the loose ball fell kindly for Azpilicueta to prod past the grounded, helpless Mat Ryan.
First-half chances were hard to come by thereafter, although Blues goalkeeper Kepa Arrizabalaga had to be alert to palm clear a Leandro Trossard effort two minutes before the break.
Not until the 80th minute was Arrizabalaga seriously tested again, scrambling to keep out half-time introduction Aaron Connolly's finish.
It was another substitute who came up with the decisive moment, though, Jahanbakhsh executing a sensational strike that left Arrizabalaga rooted.
Callum Hudson-Odoi blasted just over as Chelsea chased a winner, but they were again grateful to their goalkeeper as a point was preserved, Neal Maupay's powerful drive well blocked.
What does it mean? Rare away-day blues as Brighton rock Chelsea
Only Liverpool (25) have mustered more points away from home than Chelsea (22) this term, but Lampard must feel this was a missed opportunity. The Blues were largely comfortable until the closing stages when Brighton's substitutes wreaked havoc. With their home form a cause for concern right now, Chelsea cannot afford to throw away victories on the road.
Brighton's man of the moment
Jahanbakhsh was a club-record signing for Brighton in 2018, the deal reportedly worth £17million. That is finally starting to look like money well spent.
Emotional after breaking his duck against Bournemouth, the winger - like many in the stadium - appeared to be in a state of shock after this quite magnificent finish.
Bumbling Bissouma hooked
Mooy understandably enjoyed the majority of the plaudits following Brighton's weekend defeat of Bournemouth, but midfield colleague Yves Bissouma had been similarly impressive.
The same could not be said against Chelsea.The 23-year-old struggled with the pace of the game and lost possession 15 times, completing just 13 of his 22 passes, before he was replaced at half-time by Connolly.
Key Opta Facts
- Brighton earned their first point in a league game against Chelsea, in what was their 10th match against them.
- This was Chelsea's first away Premier League draw this season – the Blues had won seven and lost three of their 10 previous games on the road this term.
- Chelsea have scored more goals in 11 Premier League away games this season (25) than they managed on the road in the whole of 2018-19 (24).
- Azpilicueta has scored three goals in his last 11 games in all competitions for Chelsea, as many as he had in his previous 118.
- Jahanbakhsh became the fifth different Brighton player to score a Premier League goal as a substitute this season, more than any other side in the competition.
- Despite only coming on as a 68th-minute substitute, no Brighton player had more shots (3) or created more chances (3) than goalscorer Jahanbakhsh.
A hectic Premier League stretch comes to an end, but there are matches again this weekend in the FA Cup. Brighton host second-tier Sheffield Wednesday on Saturday, before Chelsea are also at home to Championship opposition in Nottingham Forest the following day.