The Blues were frustrated in a goalless first-half at Stamford Bridge, and news of Aston Villa being well on their way to victory over Tottenham only heightened the tension levels.
Harry Maguire had a goal ruled out by VAR for offside, before Tyrique George was awarded a penalty after the break after going down under pressure from Andre Onana, but that was overturned after the referee’s visit to the pitchside monitor.
With no attacking options on the bench, Chelsea’s situation was increasingly concerning for the home fans, but [Marc Cucurella](/topic/marc-cucurella) headed in with 20 minutes remaining after brilliant work from Reece James and that provided enough for a huge three points.
The result leaves Chelsea level on points with Villa but with a goal difference that is 11 better, so Enzo Maresca’s side will secure a return to Europe’s top table next season if they can win away at Nottingham Forest on the final day.
United, who host Aston Villa next weekend, now turn their attention to a Europa League final against Tottenham on Wednesday night, offering them a route back into the Champions League despite a dismal season.