The Blades looked to be done and dusted after Tammy Abraham's brace had put Chelsea 2-0 ahead at Stamford Bridge at the break, but a rousing second-half display earned United a share of the spoils.
English forward Callum Robinson, who arrived from Preston this summer, grabbed a goal back two minutes after the restart before Kurt Zouma sliced one into the back of his own net in the 89th minute, sending the travelling fans into hysterics.
Chris Wilder's men sit 10th in the table, having amassed five points from their first four games, but the bookies still believe they are in the most danger of getting relegated to the Championship.
Following closely behind at a price of 6/4 are Norwich City, who suffered their third defeat of the campaign after going down 2-0 to West Ham United at the London Stadium.
There is a feeling the Canaries will struggle to score goals if Teemu Pukki is not firing for them while the defensive frailties are a real cause for concern, with a league-high 10 goals conceded already.
With centre-back Christoph Zimmermann going off injured at the weekend, Daniel Farke is facing a selection dilemma with Grant Hanley and Timm Klose both sidelined.
Newcastle United can be found at 13/8 to get relegated and although they did pick up a point at home to Watford on Saturday, there is every chance the Magpies could drop down a level.
Switzerland international Fabian Schar cancelled out Will Hughes' effort to give Steve Bruce's men a share of the spoils but a lack of creativity on show at St James' Park looks like it will be a real issue for the north-east outfit.
Aston Villa went down 1-0 at Crystal Palace although VAR controversy once again popped its ugly head up. The visitors were denied a late equaliser after Jack Grealish was deemed to have dived on the edge of the box in the build-up to the goal.
The Villans have just one win from four games, leaving them 18th in the standings, and Dean Smith's men look like they will be in a difficult season battling against the drop.
Although sitting fourth in the table, Crystal Palace, who have recorded back-to-back victories, are expected to drop down the league and they can be found at 5/1 to be relegated.