Rosenior’s side produced one of their worst performances of a miserable season as Ferdi Kadioglu put Brighton ahead in the first half before Jack Hinshelwood and Danny Welbeck netted after the interval.
It is the first time that Chelsea have lost five consecutive league games without scoring since 1912, fittingly the year that the Titanic sank.
Beaten seven times in their last eight games in all competitions, the Blues have just one victory in their past nine league matches.
Chelsea are languishing in seventh place, seven points behind fifth-placed Liverpool in the fight for the top-five finish that guarantees a Champions League berth.
Rosenior’s team are in danger of missing out on European football altogether unless they can halt their wretched run.
They face Leeds in the FA Cup semi-finals on Sunday knowing a defeat at Wembley could push Rosenior to the brink of the sack just months after he arrived from Strasbourg to replace Enzo Maresca in January.
Rosenior this week claimed Chelsea’s owners have been “magnificent” in their backing of him despite their alarming slump.
Chelsea co-owner Behdad Eghbali has said the club remain optimistic about long-term success under Rosenior.
But the atmosphere around Chelsea is turning increasingly toxic.
Boos greeted the full-time whistle following Saturday’s 1-0 defeat to Manchester United at Stamford Bridge after supporters staged a protest against owners BlueCo ahead of kick-off.
There were more jeers for Rosenior and his players from Chelsea’s fuming fans at Brighton, who climbed above the Blues into sixth place. (AFP)