Bournemouth were made to rue a series of missed chances in a 2-1 defeat at a much-changed Manchester City that sends the Cherries closer to the Championship, while Wolves' hopes of a top-four Premier League finish slipped away after conceding a controversial late penalty to draw at Burnley on Wednesday.
Tottenham also aided their quest to qualify for next season's Europa League as Harry Kane scored twice in a 3-1 win at Newcastle.
City enjoyed a far bigger win off the field already this week with their appeal to the Court of Arbitration for Sport overturning a two-season ban from playing in European competitions, freeing up Pep Guardiola's men to play in the Champions League next season.
Guardiola showed his immediate focus is on winning another trophy with an FA Cup semi-final against Arsenal to come on Saturday.
Aymeric Laporte, Kevin De Bruyne, Raheem Sterling and Riyad Mahrez were all left on the bench to keep them fresh for Wembley, but City still had too much quality in the form of David Silva and Gabriel Jesus.
Silva has just two more matches at the Etihad after a 10-year City career and showed why he will be so missed by curling a free-kick in off the underside of the crossbar six minutes in.
Bournemouth have given themselves a chance of beating the drop by taking four points from their previous two games against Tottenham and Leicester.
Eddie Howe's men had chances to level against a makeshift City defence as Ederson turned Junior Stanislas's free-kick onto the post before Nicolas Otamendi's last-ditch challenge diverted Dominic Solanke's goalbound shot over.
At the other end, Jesus was ruthless as he wriggled between two weak Bournemouth challenges inside the box before firing into the far corner to score for the third consecutive game.
Bournemouth could still have claimed a vital point in their battle to beat the drop thanks to a spirited second-half display. VAR ruled out Josh King's strike by the narrowest of margins for offside before City also had a penalty denied by a VAR review.
City finally conceded for the first time in five home games since the restart when David Brooks turned home Callum Wilson's cross two minutes from time before Wilson fired the best of a host of late chances for the visitors wide.
Defeat leaves Bournemouth still three points adrift of safety from Watford and West Ham, who face each other on Friday.
Wolves remain three points adrift of the Champions League places with just two games to play after Chris Wood's 95th-minute spot-kick salvaged a 1-1 draw for Burnley.
Nuno Espirito Santo's men were dominant throughout with Raul Jimenez and Adama Traore a constant threat, but it was not until 14 minutes from time that the visitors broke the deadlock thanks to Jimenez's stunning strike on the half-volley.
Wood thought his chance to snatch a draw had gone when he somehow headed wide with the goal at his mercy in stoppage time.
But there was still time for a final twist when Mike Dean pointed to the spot for a handball by Matt Doherty despite the Irishman seemingly being impeded by Wood's attempt at an overhead kick.
Jose Mourinho secured his first ever win at St James' Park to keep Tottenham's chances of European football next season on track by moving up to seventh.
Kane and Son Heung-min were again the deadly duo for Spurs as the South Korean's low strike that crept in at Martin Dubravka's near post opened the scoring.
Serge Aurier started for the visitors just three days after his brother was shot dead in Toulouse and the Ivorian right-back was at fault for Newcastle's equaliser as Matt Ritchie pounced on a wayward clearance to fire into the top corner.
However, Kane quickly restored Tottenham's lead with a back-post header and the England captain showed great bravery to add a second with his head in the final minute as he clashed with Fabian Schar.