Chelsea were held to a 0-0 draw by Norwich at Stamford Bridge, where Andre Schurrle and David Luiz hit the woodwork.
Both teams needed three points for very different reasons, with Chelsea trying to keep the pressure on title rivals Manchester City and Liverpool, and Norwich looking to move out of the relegation zone.
Chelsea huffed and puffed but could not break down a resolute Norwich defence, for whom Michael Turner excelled.
Schurrle beat John Ruddy but hit the upright with a right-footed shot in the first half, while second-half sub Luiz smacked the crossbar with a fierce drive.
Both teams had strong shouts for a penalty turned down by referee Neil Swarbrick, but in truth neither side showed the quality or desire to earn three crucial points.
Chelsea's last game of the season is away at relegated Cardiff, while Norwich welcome Arsenal to Carrow Road knowing even victory may not be enough to save them.
Arsenal coasted to a 1-0 win over West Brom in their final Barclays Premier League home match of the season at the Emirates Stadium.
Following Everton's defeat by Manchester City on Saturday, the Gunners were already secure of fourth spot, and with it a chance of qualifying for the Champions League group stages once again next season.
Olivier Giroud headed in his 22nd goal of the campaign in all competitions after 14 minutes, which proved enough to see off West Brom, who are all but secure of their top-flight status with two matches left still to play.
Hull and Aston Villa are assured Barclays Premier League football next season after Norwich failed to win at Chelsea.