Manchester United reduced the gap on fourth-placed Manchester City to one point with a 1-0 win over a Norwich side that now seem doomed.
United needed a win to keep the pressure on their neighbours for the final Champions League place and, although it was far from a classic display, Juan Mata brought back the points after capitalising on Sebastien Bassong’s error at the back.
The Canaries are not mathematically down but are four points away from safety and their fate lies in the hands of others.
West Ham lost their penultimate game at Upton Park as Swansea claimed a 4-1 win to dent the home side’s European ambitions.
The visitors were two up at half-time through Wayne Routledge and Andre Ayew.
Ki Sung-yeung then made it 3-0 before Hammers substitute Diafra Sakho and Swansea striker Bafetimbi Gomis added to the scoreline.
Crystal Palace were 2-1 winners over Stoke at Selhurst Park, formally ensuring survival, with Dwight Gayle making a timely case for an FA Cup final starting spot.
He scored both of his side’s goals in the second half to overturn a Potters lead earned through Charlie Adam’s 27th-minute effort.
Bournemouth and West Brom, two sides who have already achieved their primary aim for the season by surviving, drew 1-1 at Dean Court.
Salomon Rondon gave the Baggies a 16th-minute lead but Craig Gardner spurned the chance to double the lead from the penalty spot.
Substitute Matt Ritchie made him rue that miss by grabbing an equaliser eight minutes from time.