It was telling of the early season pressure on both Ole Gunnar Solskjaer and Frank Lampard that both sides were reluctant to leave themselves exposed.
However, the Blues will feel they were denied a clear penalty following Harry Maguire's first half WWE effort on Cesar Azpilicueta.
That incident can be seen below:
Per Goal's Chelsea correspondent Nizaar Kinsella, the Professional Game Match Officials Board (PGMOL) have since confirmed that VAR did check the incident but decided it wasn't worthy of a spot-kick.
It's not the first time Maguire has benefited from a questionable VAR decision against Chelsea either, having got away with his kick on Michy Batshuayi last season.
United might argue they ought to have had a penalty of their own, Marcus Rashford hitting the deck after a coming together.
In the Sky Sports studio, however, even Patrice Evra declared that Rashford's appeal was soft but that Maguire was guilty of a clear foul.
The Red Devils did have other chances, Edouard Mendy at full stretch to deny Juan Mata and also doing very well to block Rashford's shots - including a long-range effort in injury time.
That provided the Chelsea stopper with a chance to redeem himself after he'd channeled his inner Kepa and nearly passed the ball into his own net. A moment of madness saw the 'keeper put it out for a corner after mindlessly passing across his goal.
But such flashes of excitement were few and far between.
Chelsea had reverted to five at the back and looked hesitant to attack.
Solskjaer did hand a debut to Edinson Cavani, who nearly scored with his first touch but put it into the side netting.
Overall, though, there was little to buoy United - it's the first time in 48 years that they've failed to win any of their opening three league games of a season - but it will come as a relief to Solskjaer at least that Maguire went unpunished.
The centre-back has had a terrible start to the season following his summer arrest in Greece. While he somewhat redeemed himself with a goal against Newcastle, he'd have been in the spotlight yet again had the right decision been made at the Theatre of Dreams.
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