Tammy Abraham's last-gasp goal completed Chelsea's rescue mission following a shambolic first half in a breathless 3-3 draw at West Brom.
The Baggies were gifted three goals inside 27 minutes at The Hawthorns with Callum Robinson scoring twice after shoddy defending from Marcos Alonso and 36-year-old Premier League debutant Thiago Silva.
Kyle Bartley made it 3-0 after more poor work at a corner but Mason Mount's well-struck 55th-minute effort was backed up by substitute Callum Hudson-Odoi putting the finishing touch on a great Chelsea move.
West Brom then buckled under the sheer weight of pressure in five additional minutes as Abraham tapped in from close range after Sam Johnstone saved Mount's shot.
Robinson caught Chelsea cold inside four minutes with a fine drilled finish across Willy Caballero after Matheus Pereira had picked off Alonso's poor header.
Abraham missed a sitter and Timo Werner wastefully crashed against the crossbar before another error, this time Silva's dallying and slip, allowed Robinson to slide under Caballero to double the lead.
Incredibly it was 3-0 when Bartley unerringly slotted in from Darnell Furlong's downward header at Pereira's corner with Chelsea's defending again suspect.
Alonso and Mateo Kovacic were sacrificed for Cesar Azpilicueta and Hudson-Odoi at the break and a high-tempo Chelsea reduced the arrears with a crisp long-ranger from Mount that left Johnstone flat-footed.
A fine Chelsea move culminated in Hudson-Odoi linking brilliantly with Kai Havertz before coolly finding the bottom-right corner to really get West Brom nerves jangling with 20 minutes to go.
West Brom were penned further and further back as time wound down and Abraham earned Chelsea the point after reacting quickly when Johnstone could only parry Mount's effort, with a VAR check ruling Havertz had not handled shortly before.
What does it mean? Big-spending Blues must gel quickly
Chelsea may have just avoided defeat but after Lampard was backed by a spending spree in excess of £200 million he will not have the luxury of the patience he was afforded last season.
With new recruit Ben Chilwell to come in at left-back and Edouard Mendy surely to take over in goal after arriving from Rennes – with Kepa Arrizabalaga again benched – you would expect Chelsea to shore up. They must do so quickly.
And here's to you Callum Robinson…
Robinson has three Premier League goals to his name, all against Chelsea (one was for Sheffield United). His first was, in truth, only a half chance despite Alonso's helping hand and he scored with both of his shots on target, while West Brom netted with all three of theirs as a team.
Lampard has no case for the defence
Silva was brought in on a free transfer to shore up a leaky backline as Chelsea spent big elsewhere. He was far from the only culpable party in a mind-boggling show of first-half ineptitude but he certainly did not help.
Chelsea have made three errors leading to goals this term, the same amount as the whole of last season. Throw in 42 away goals conceded since the start of last season, more than any other side, and there are still big defensive concerns for the Blues.
Chelsea switch focus to Wednesday's (AEST) EFL Cup fourth-round tie at Tottenham, while West Brom are next in action at Southampton in the Premier League on October 4.