Chelsea continued their unbeaten start to life under Thomas Tuchel after surviving a bizarre own goal from Antonio Rudiger.
Sheffield United almost caught the visitors cold inside 30 seconds after recovering possession on the halfway line.
Oli McBurnie set Oliver Burke racing away, but the Blade lashed his effort into the side netting to give Chelsea a huge let off.
The Blues soon clicked into gear, and came close to breaking the deadlock through Timo Werner.
Set free by a lofted ball from Mateo Kovacic, the German chipped the onrushing Aaron Ramsdale. His strike lacked power, however, affording Chris Basham the opportunity to hook the ball to safety.
Sheff Utd thought they’d been awarded a penalty moments later after Basham was felled in the box by the recalled Ben Chilwell. VAR came to the England left-back’s rescue with Basham judged to have been offside in the build-up.
The game then settled into a familiar pattern of play for much of the first half. Chelsea dominated the ball, often seeing their possession stat hit the high seventies. Clear-cut chances were proving difficult to come by though. As half-time approached, just one effort on target had been registered.
Chilwell began to venture further forward down the left, but the offside trap put an early halt to one promising opportunity.
Content with soaking up pressure, the hosts sat deep and bided their time hoping to get to half-time level.
The strategy seemed destined to succeed, but with two minutes remaining, Chelsea finally found their cutting edge.
Werner broke free down the left before his accurate cut-back found Mason Mount on the edge of the box.
The England midfielder expertly steered a first-time left-footed strike into the bottom corner to make it 1-0.
The Blades emerged with renewed vigour after the interval and were gifted a leveller in truly comical fashion.
A ball played through should’ve been light work for Antonio Rudiger to deal with.
The German inexplicably opted to pass back to Edouard Mendy, but the goalkeeper had himself rushed off his line to scoop up the loose ball, ensuring a bizarre own goal was scored.
Chelsea hit back immediately and were awarded a penalty after a brief VAR check when Ramsdale toppled Werner inside the area. The forward was alert and latched on to an errant back-pass to force an issue strikers with a lower workrate would not have caused.
Jorginho assumed the responsibility and with his trademark hop, skip and a jump, rolled the ball into the net after sending Ramsdale the wrong way.
John Fleck blazed a trail through the Chelsea backline into the box, but Rudiger, atoning for his error, blocked the resulting effort as the game entered its final stages.
Werner was replaced by N’Golo Kante and gave Chelsea fans cause for concern when being spotted having his thigh strapped in the stands.
Despite their best efforts, the hosts couldn’t mount a fightback, ensuring Chelsea emerged with all three points via a 2-1 scoreline.