The result opens up a significant gap in the race for the top five, with United pulling clear while Chelsea's hopes of reaching Europe's elite competition continue to fade after a fourth successive Premier League defeat without scoring.
Despite dominating large spells of the contest, Chelsea were once again left to rue their lack of cutting edge. Liam Rosenior's side created the better chances, struck the woodwork multiple times and finished with superior possession and expected goals, yet failed to find the net for the fourth game running.
Their frustration was evident both on and off the pitch. Hundreds of supporters had protested against the club's ownership before kick-off, and the mood inside Stamford Bridge turned increasingly toxic as missed opportunities piled up. Boos rang out at full-time, accompanied by chants demanding change.
Chelsea started brightly and should have taken the lead early on. Estevao Willian clipped the outside of the post before being forced off with a hamstring injury, while Enzo Fernandez squandered a clear opening from close range. Liam Delap also had an effort ruled out for offside and later hit the crossbar with a header as the hosts piled on pressure.
Yet for all their attacking intent, it was United who struck with ruthless efficiency. With Wesley Fofana temporarily off the pitch receiving treatment, space opened up in Chelsea's defence and Bruno Fernandes capitalised, cutting the ball back for Cunha to fire home first time. It was United's only shot on target of the match, and Fernandes' 18th league assist of the season.
The visitors offered little going forward beyond that moment but defended resolutely. An improvised back line, featuring strong performances from Ayden Heaven and Noussair Mazraoui in central roles, stood firm under sustained pressure to secure a rare clean sheet.
Chelsea continued to push after the break, with Cole Palmer and Delap both going close, while another effort rattled the woodwork. However, their inability to convert chances proved costly once again.
For United, the victory marks a timely return to form and reinforces their position among the league's top sides, with belief and organisation proving decisive. For Chelsea, the outlook is far bleaker. Now trailing their rivals by a considerable margin and slipping behind in the race for fifth place, their season is in danger of unravelling completely unless they rediscover both confidence and a cutting edge in front of goal.