The Carling Cup has been boom or bust for Chelsea since 2004-05 and last night it was bust again as they went out at home to Burnley, of the Coca-Cola Championship.

Winners twice and losing finalists once in the past four seasons, Chelsea also recorded the only domestic home defeat in José Mourinho’s time as manager in this competition, when they were eliminated on penalties by Charlton Athletic after a 1-1 draw in the third round in October 2005.

When last night’s match finished on the same score after 90 minutes, many sensed a repeat and almost expected Burnley to add the scalp of the Barclays Premier League leaders to those of Liverpool, Aston Villa and Fulham, their victims in recent seasons, and so it proved as Brian Jensen, the Burnley goalkeeper, saved Chelsea’s first penalty in sudden death, from John Obi Mikel, to send his side through to the quarter-finals.

Didier Drogba’s first goal of the season, after 27 minutes, had looked as if it would be enough to send Chelsea through to the last eight until Burnley struck back after 69 minutes through Ade Akinbiyi, a substitute.

Luiz Felipe Scolari had said that he was taking the competition seriously, as befitted the manager of a club with Chelsea’s recent record. Even so, he rested Nicolas Anelka in order to restore Drogba to the starting line-up for the first time since he injured a knee in a Champions League tie away to CFR Cluj on October 1 and began with John Terry and Frank Lampard on the bench. Scolari also gave a first start to Mineiro, the 33-year-old former Brazil midfield player, whom he signed as a free agent in September, ostensibly to cover for the absence through injury of Michael Essien, although in appearance and playing style Mineiro evoked memories of Claude Makelele.

Burnley, though, commanded respect. They occupy fifth place in the Championship and had not conceded a goal in their three matches in the Carling Cup, the most recent a 1-0 victory over Fulham, Chelsea’s neighbours.

It took Chelsea 14 minutes to test Jensen and when they did he came through with flying colours. Drogba’s pass put Salomon Kalou through on goal, but Jensen met him just outside the penalty area, executing a tackle of which any central defender would have been proud.

However, Jensen was beaten after 27 minutes when Lampard, who had come on two minutes earlier in place of the injured Juliano Belletti, played a pass forward to Drogba. The Ivory Coast forward jinked inside Michael Duff 18 yards out and, as other defenders rushed across to cover, curled his shot out of the goalkeeper’s reach to score his first goal of the season.

It could have been 2-0 shortly afterwards as Jensen had to save at full stretch from Kalou when he shot fiercely for the bottom far corner, and the goalkeeper was lucky that the rebound eluded Drogba.

Burnley appealed half-heartedly for a penalty when Martin Paterson fell over a challenge from Lampard, but they almost conceded again when Branislav Ivanovic met Florent Malouda’s cross with a diving header that looped up and over Jensen and came back off the bar.

Jensen is nicknamed “The Beast” and he showed his teeth when he reacted angrily to a challenge by Kalou before counting to ten. It was as well that he kept a cool head, for after 69 minutes his team were level.

An angled cross-shot by Chris Eagles was parried by Carlo Cudicini and it was the Chelsea goalkeeper’s bad luck that it fell kindly for Akinbiyi, who had been on the pitch only nine minutes. Showing a coolness in front of goal that has not always been his hallmark, Akinbiyi side-footed calmly into the corner of the net in front of 6,000 travelling fans packed into the Shed End. Chelsea pressed hard for a winner but Burnley were able to soak up pressure.

Lampard had the ball in the net early in extra time, only to be flagged offside, and chances began to arrive as both teams tired. Akinbiyi’s glancing header from Graham Alexander’s cross was well held by Cudicini and it seemed that Alex must win it for Chelsea when he met a cross from the left, only to scoop the ball over the bar from a yard out.

Three minutes from the end of extra time, Steven Caldwell, the Burnley captain, was sent off after being shown a second yellow card for a foul on Malouda. It seemed a harsh decision by Keith Stroud, the referee, and it could have been even more costly when Lampard belted the resulting free kick past the wall and through a crowd. Jensen must have seen it late, but somehow he held the ball at the second attempt with a scrum of Chelsea players bearing down on him.

And so to penalties. Jensen saved the second of Chelsea’s initial five, from Wayne Bridge, but Wade Elliott shot over the bar when he had the chance to clinch the shoot-out. “He did the same in training, but I fancied him to score tonight,” Owen Coyle, the Burnley manager, said.

Fortunately for them, it did not matter. Duff scored to put Burnley 5-4 ahead in sudden death and Jensen leapt acrobatically to his right to knock away Mikel’s effort to secure their passage. “We didn’t practise penalties,” Coyle added. “Who thought we’d get that far?”

Chelsea (4-1-4-1): C Cudicini - P Ferreira, Alex, B Ivanovic, W Bridge - Mineiro - S Kalou, Deco (sub: J O Mikel, 46min), J Belletti (sub: F Lampard, 25), F Malouda - D Drogba (sub: F Di Santo, 70). Substitutes not used: Hilário, J Terry, M Woods, S Sinclair.

Burnley (4-4-2): B Jensen - G Alexander, M Duff, S Caldwell, S Jordan - W Elliott, J Gudjonsson (sub: K McDonald, 97), C McCann, C Eagles - R Blake (sub: A Mahon, 76), M Paterson (sub: A Akinbiyi, 60). Substitutes not used: D Penny, A Kay, A MacDonald, J Rodriguez. Booked: Caldwell, Eagles, Akinbiyi. Sent off: Caldwell.
Referee: K Stroud.