Kepa Arrizabalaga saved Chelsea from defeat with a string of fine saves as the west Londoners ran out of steam at the Amex Stadium but came away with a point in a 1-1 draw with Brighton thanks to an early strike by skipper Cesar Azpilicueta.
Having won at Spurs and Arsenal in recent weeks, Chelsea were confident of making it three on the bounce away from home - but their inability to kill the game off, came back to haunt them when substitute Alireza Jahanbakhsh stuck a wonderfully acrobatic overhead kick to level the score in the second half.
From that point on, it was all the home side, but Kepa foiled the Seagulls an numerous occasions to keep the Blues firmly in fourth place in the Premier League.
Chelsea started brightly - a fine passage of play involving Cesar Azpilicueta and N’Golo Kante saw Reece James bomb forward, but his shot was weak and misdirected and drifted harmlessly wide of Mathew Ryan’s left upright.
The home side’s first effort came two minutes later on five minutes but Steven Alzate’s low right-footer zipped inches wide of Kepa’s right post.
The first Premier League goal the new decade came on 10 minutes when Azpilicueta was on the spot to smash home from close range after Willian’s corner was headed back into the mix by Kurt Zouma. The Seagulls failed to clear, and the Spain left wing back put the Blues 1-0 ahead.
Tammy Abraham picked the pocket of Davy Propper on 27 minutes. He raced forward with Willian supporting on the right. The striker opted to try an edge of penalty area shot - it was goal bound but took a deflection for a corner. Willian’s unhappy look at Abraham for failing to pass to him was clear for all to see.
Three minutes from the break, Brighton had their best chance of the game - Leandro Trossard smacked a first-time curling left-footer from just inside the Chelsea penalty area. Kepa was equal to the fine shot, by parrying it away from goal, with a spectacular dive to his left.
Pulisic had the first effort of the second half, Ryan did well at his near post to thwart a low left-footer from the American.
He had another effort on 54 minutes, which zipped inches past the same right upright.
This was quickly followed by a Kante shot - that was the best it got for the visitors.
All the time, Brighton still posed a threat when counter-attacking.
Frank Lampard decided that Pulisic had had enough and opted to replace him with Callum Hudson-Odoi on 66 minutes.
Mason Mount, by his own standards, played a poor game and was replaced by Mateo Kovacic with 18 minutes left on the clock.
Kepa produced another wonderful save to foil substitute Aaron Connolly as the home side started to rattle the Chelsea rearguard. Kepa managed to get low to his right to tip away Connolly’s scuffed right-footer from close range.
The breakthrough happened with seven minutes left, from a regulation corner, Jahanbakhsh produced a spectacular overhead kick from just inside the Chelsea area. The ball arrowed into the far corner of Kepa’s net.
Kepa kept the Blues in the game when he hacked away a low rasper from Neal Maupay late on.
Chelsea clung on to take the point back down the M23 and now have to rest, recharge their batteries and prepare for Sunday’s home FA Cup match against Nottingham Forrest
Teams: Chelsea, Kepa, Rudiger, Jorginho, Kante, Abraham, Willian, Zouma, Mount, Pulisic, James, Azpilicueta
Subs: Caballero, Christensen, Kovacic, Hudson-Odoi, Batshuayi, Emerson, Lamptey
Brighton: Ryan, Dunk, Maupassant, Bissouma, Trossard, Webster, Mooy, Montoya, Propper, Burn, Alzate
Subs: Button, Duffy, Stephens, Gross, Jahanbakhsh, Bernardo, Connolly
Referee: Stuart Atwell