Albion's record signing Jahanbakhsh had broken a 20-match league duck with his strike in the 2-0 win over Bournemouth on December 28. And the 28-year-old started 2020 in some style, with a bicycle kick finish worthy of anyone's highlights reel.
Captain Cesar Azpilicueta tapped home just nine minutes in as Chelsea dominated the opening hour. But by the final whistle it was the Blues who were clinging on, to leave Brighton buoyed by the point but Chelsea frustrated not to grind home.
Christian Pulisic will look at three wasted openings that ultimately stopped the Blues cementing their dominance, denying Lampard's side another quickfire away victory after Sunday's 2-1 win at Arsenal.
Azpilicueta did the honours with the first Premier League goal of 2020, tapping in a facile finish from a corner following a goalmouth scramble.
The 30-year-old toasted his 100th start as Blues captain in style and Chelsea seized on their early opener to squeeze themselves into total control.
A sprightly Pulisic dragged wide from a well-worked and promising position, and the USA forward would have expected to hit the target.
The Blues turned around far the happier in their 1-0 advantage, but could perhaps have anticipated boss Lampard firing a warning shot against complacency.
Yves Bissouma perhaps best summed up Chelsea's dominance with a weary shrug of the shoulders after the last of many mini run-arounds from Jorginho.
The Albion struggler was taken off at the break with Aaron Connolly on to stiffen the home midfield, but after the interval Chelsea still picked up where they had left off.
Pulisic had tormented Martin Montoya throughout the first-half and extended the Brighton man's torrid time by outfoxing him twice in quick succession after the break.
Chelsea's USA forward failed to find the target on both occasions however, with the Blues' missed chances starting to mount.
The visitors survived Jorginho being mugged by Maupay in his own half in a rare error from the Italy midfielder.
Pulisic drew a save from Mathew Ryan after a scything ball from Willian, but that proved his last act of the day as Callum Hudson-Odoi climbed off the bench to add final quarter impetus.
Mateo Kovacic then replaced Mason Mount in a defensive move from Lampard aimed at shutting the contest down.
Brighton finally sensed Chelsea's disquiet and Connolly almost fired an equaliser, only for Kepa to produce a fine point-blank save.
Kovacic had conceded the free-kick for Connolly's chance, and then made another cheap and risky foul within shooting range.
Trossard wasted the opportunity to hand both Kovacic and Chelsea a serious let-off.
The Blues ignored all the warning signs though, and paid the price when Jahanbakhsh pulled off a fine bicycle kick to volley Brighton level.
A floundering Chelsea almost threw the game away entirely at the death, as Maupay was thwarted by another good Kepa save.
But the visitors held on amid the onslaught, for a point not to be sniffed at but entirely two that they dropped.