Fulham recorded back-to-back wins for the first time this season with a 1-0 victory on the south coast at Bournemouth.
Elsewhere, Watford breezed past the relegated Huddersfield thanks to a double from Gerard Deuleufeu.
While Leicester secured a last-gasp draw at the London Stadium thanks to a late strike from Harvey Barnes.
Wolves were held 0-0 at Molineux by relegation threatened Brighton.
BOURNEMOUTH 0-1 FULHAM
Relegated Fulham ruined Eddie Howe’s 500th match as a manager by ending a year-long wait for an away win with a 1-0 success at Bournemouth.
Aleksandar Mitrovic’s second-half penalty gave the 19th-placed Cottagers a first league victory on the road since beating Millwall in the Sky Bet Championship on April 20 last year.
The Serbia international converted from the spot after being brought down by Cherries substitute Jack Simpson to halt a goal drought dating back to January.
Victory at the Vitality Stadium, which spoilt the landmark occasion for Cherries boss Howe, strengthened the hopes of Fulham caretaker boss Scott Parker landing the job on a permanent basis.
After beginning his Craven Cottage tenure with five consecutive defeats, Parker has now guided the west London club to successive league victories for the first time since promotion last May, restoring some pride at the end of a torrid season.
HUDDERSFIELD 1-2 WATFORD
Gerard Deulofeu’s double earned Watford a 2-1 win at Huddersfield, who slumped to a record-equalling Premier League defeat.
Deulofeu produced a finish similar to his stunning effort at Wembley earlier this month in Watford’s FA Cup semi-final win over Wolves to give his side an early lead.
The Spaniard then sealed the points for the Hornets with 10 minutes to go before Huddersfield substitute Karlan Grant headed a stoppage-time consolation.
Watford’s sixth win on the road this season kept them on course for their highest Premier League finish, while relegated Huddersfield matched another unwanted record.
The Terriers, who became only the second club after Derby in 2008 to be relegated from the Premier League in March, lost their 14th league game at home this season to match Sunderland’s mark set in 2002/03 and 2004/05.
WEST HAM 2-2 LEICESTER
Harvey Barnes pulled the rug out from under West Ham as Leicester snatched a 2-2 draw at the London Stadium.
The 21-year-old substitute grabbed his first Foxes goal in stoppage time to salvage a point for Brendan Rodgers’ side.
Jamie Vardy had earlier cancelled out Michail Antonio’s first-half header before Lucas Perez fired West Ham back in front nine minutes from the end
It was a lively end to a match which for long periods had all the hallmarks of an end-of-season run in the sunshine.
WOLVES 0-0 BRIGHTON
Brighton secured a crucial point in their battle against relegation after frustrating Wolves at Molineux.
The hosts had spent the week training in Marbella and went go-karting in their free time but stalled badly in a 0-0 draw with the Seagulls.
A hard-earned draw ended Brighton’s run of five straight defeats in all competitions and moved them three points ahead of Cardiff, who host title-chasing Liverpool on Sunday.
Diogo Jota twice hit the woodwork and Leander Dendoncker was denied by Mathew Ryan but the hosts dropped to ninth after an instantly forgettable stalemate.