Chelsea's season was in danger of hitting a new low when their latest defensive calamity allowed David Murphy to give the Blues a shock half-time lead at Stamford Bridge.
Colin Doyle also brilliantly saved a Juan Mata penalty and, although Daniel Sturridge eventually equalised, Chelsea simply did not do enough to find a winner.
The performance showed Sunday's summit meeting in which Andre Villas-Boas' players reportedly challenged their manager did nothing to address the problems which led to their worst display of the season at Everton last weekend.
Villas-Boas insisted it did not matter if some of his squad did not back him as he had the support of Roman Abramovich, but the club's billionaire owner would not have been happy with what he saw.
The man he spent £50million on - Fernando Torres - again failed to impress, hauled off at half-time for Didier Drogba, who was a surprise substitute following the African Nations Cup.
But others, too, let themselves down as Chelsea's winless run extended to four matches.
The travelling fans taunted Villas-Boas with chants of, "You're getting sacked in the morning", as Chelsea toiled from the start.
The hosts were almost embarrassed when David Luiz's attempted clearance deflected off a Blues head before Stephen Carr was forced off injured, Jonathan Spector coming on.
The defending that cost Chelsea at Goodison Park resurfaced when they fell behind in the 20th minute, Luiz and Raul Meireles failing to deal with a near-post corner, allowing Murphy to drill home.
Chelsea finally woke up and urgent attacking immediately won them a penalty when Wade Elliott tripped Ramires but Doyle produced a world-class save to tip Mata's spot-kick onto the post.
Curtis Davies produced a brilliant interception to stop Torres reaching a cross from Sturridge, who then screamed in vain for another penalty when he crumpled under Pablo Ibanez's challenge.
Luiz tried to inject some inspiration when a typical surge forward saw Jordon Mutch rightly booked for the crudest of challenges, which the defender almost punished with a superb free-kick that Doyle tipped over.
Sturridge then unleashed a blistering volley that just dipped too late and Mata directed a header too close to Doyle before Chelsea trudged off to muted jeers.
The boos turned to cheers after the interval when Torres, who had another half to forget, was hauled off for Drogba.
The Ivorian immediately showed the kind of commitment lacking from Torres by retrieving the ball for a goal-kick.
But Chelsea showed little sign of improvement and Gary Cahill was booked for a tangle with Adam Rooney before more shocking set-piece defending saw Redmond blast over a corner.
Salomon Kalou replaced the ineffective John Obi Mikel, although it was someone else the crowd wanted, judging by the chants of "Super Frankie Lampard".
However, the change paid off, Mata drilling wide after brilliantly taking down Luiz's crossfield pass before Sturridge equalised in the 62nd minute.
Branislav Ivanovic was given time to deliver a cross and Sturridge rose unmarked to power home a header via the inside of the post.
Elliott threw himself in front of Ivanovic's attempted follow-up before Rooney was withdrawn for Jake Jervis.
Meireles' low drive through a crowd of players was deflected just over the bar while Mutch tested Petr Cech with a low free-kick.
Lampard finally joined the fray when he replaced Mata for the last seven minutes in another unpopular substitution, with Elliott also withdrawn for Chris Burke.
Ivanovic appealed half-heartedly for a penalty after a coming together with Murphy before Blues wasted a glorious chance to snatch it when Redmond shot tamely at Cech after racing clear.
Lampard drilled a free-kick straight at the wall in stoppage-time, Luiz was cautioned for clattering into Spector, and Davies headed too close to Cech as Blues held on for a deserved replay.
Source: PA