Chelsea and Norwich City were left hanging on to their respective targets by their fingertips after their Premier League match ended goalless at Stamford Bridge.
Chelsea had the better chances to win a tense match hitting the woodwork twice through Andre Schurrle and David Luiz.
The Londoner's slim hopes of winning title are all but over as they now need to win their last match at relegated Cardiff City and hope that both the top two, Manchester City and Liverpool pick up no more than one point from their last two matches.
Manchester City lead the standings with a superior goal difference from Liverpool with both on 80 points from 36 matches.
Avoiding the drop
Norwich can only avoid joining already relegated Cardiff City and Fulham in the Championship next season if they beat Arsenal next week and Sunderland lose both of their remaining fixtures.
They have 33 points, two behind Sunderland, who are one place above the relegation zone after a 1-0 victory at Manchester United.
The fact Norwich did not win at Chelsea means that Aston Villa and Hull City cannot be relegated and West Brom are effectively safe as well.
In the day's earlier match a first half header from Olivier Giroud gave Arsenal a 1-0 win over West Bromwich Albion in a largely uneventful end-of-season stroll in the sun at the Emirates Stadium.
Arsenal, who have 76 points, will now finish fourth, ensuring them of a 17th successive season in the Champions League next season.