Shakhtar Donetsk condemns Chelsea
The Blues were ruthlessly punished by Teixeira and Fernandinho goals at the Donbass Arena, despite Oscar's late consolation, as Shakhtar deservedly took charge of Champions League Group E in the first of what could be a crucial double-header.
Chelsea were spared dropping out of the qualification places by Juventus' shock draw at Nordsjaelland, but they will need to do much better at Stamford Bridge in two weeks to avoid doing so.
Terry's first appearance since accepting his racism ban got off to the worst possible start as he unwittingly set up Shakhtar's opener inside three minutes.
But he was arguably the least culpable Chelsea player on a night which cost the Barclays Premier League leaders dearly and a risible performance from Fernando Torres scuppered their hopes of a comeback.
The defeat was their first since their UEFA Super Cup thrashing by Atletico Madrid and the performance was almost as alarming at times as they were carved open by an outstanding Shakhtar side.
The build-up to the game was predictably dominated by Terry's return, the timing of which was quite extraordinary.
It not only coincided with his four-match domestic ban for racially abusing Anton Ferdinand, but came a year to the day since the offence took place and also saw him take part in an initiative in which he wore a 'Unite Against Racism' armband.
The race row was the lowest point of Terry's already-checkered career, making Tuesday night's game arguably the biggest test yet of his legendary ability to thrive under pressure.
It was also against opponents on a quite extraordinary run, Shakhtar having not lost for exactly 11 months while winning their last 21 league games.
And it was a nightmare start for the defender as the home side scored from their first attack after two minutes and 53 seconds, Luiz Adriano's shot hitting Terry's elbow and falling perfectly for Teixeira to slot past a helpless Petr Cech.
In what was a fiercely-contested game in a fizzing atmosphere, Oscar tried to respond with a tame low drive before Willian almost lived up to his manager's promise to make Chelsea pay for not signing him by drilling wide.
That was in the 15th minute and it immediately got worse for the visitors when Frank Lampard went down injured, forcing an early end to his record 100th European appearance for the club and the introduction of Eden Hazard.
Ashley Cole was then needlessly booked for dissent as the relentless action surged from end to end, Torres wasting a great chance either to score or set up a team-mate before Terry twice produced vital blocks to prevent Shakhtar adding to their lead.
His early misfortune aside, Terry was having a stellar game, repeatedly reading attacks.
But he could not stop Willian brilliantly setting up Henrik Mkhitaryan, Cole doing enough to force Shakhtar's goal machine to shoot too close to Cech.
That sparked a flurry of chaotic corners, which Chelsea defended frantically and saw Cech produce a wonder-save to deny Tomas Hubschman from point-blank range after Oscar inadvertently set up the midfielder.
Torres' weak hooked volley from Branislav Ivanovic's cross summed up a half in which he proved a real liability, a theme that continued after the restart.
Chelsea were otherwise looking capable of equalising, Juan Mata firing over after good work from Hazard, who immediately produced a horrendous gaffe to gift Shakhtar their second goal in the 52nd minute.
He was pickpocketed in the center circle by Fernandinho, who fed Adriano and both raced goalwards for the former to slot past Cech.
Hazard tried to make amends with a low drive tipped wide by Andriy Pyatov, who then palmed a Ramires blockbuster behind for a corner.
Shakhtar weathered the storm, although Olexandr Kucher was booked for cynically bringing down Hazard and John Obi Mikel hooked over a chance for his first ever Chelsea goal.
Torres was finally withdrawn for Daniel Sturridge with 20 minutes remaining and Mkhitaryan twice went close to making it 3-0.
Hazard scuffed a great chance to make him rue the miss, Hubschman almost bundled home a third for Shakhtar and Hazard was thwarted one-on-one with Pyatov.
David Luiz and Hubschman were both booked in the closing stages, which saw Oscar set up a tense finish two minutes from time when he swept home Ivanovic's cross.
Information from The Associated Press was used in this report.