Two more Tammy Abraham goals had the Blues in front at half-time, but Sheffield United fought back after the interval and scored at the beginning and the end of the second period to earn a draw.
Abraham showed typically predatory instincts to fire in his maiden Stamford Bridge goals, one shortly before the 20-minute mark and the other with half-time approaching.
It had been another enjoyable Chelsea performance up to that point, but the Blades carried a threat too and they halved the deficit immediately after the interval through Callum Robinson.
Abraham came as close as anyone to restoring our two-goal advantage but he was denied from close range by Dean Henderson, a long-time team-mate of his in England's youth teams.
We had done well to restrict the visitors to long-range efforts in the closing stages, but with two minutes left Kurt Zouma could only divert Robinson’s teasing cross into the net. There was no time left for a winner.
So a second straight home draw at the start of this Premier League campaign. It’s the international break now before a trip to Wolves in a fortnight’s time.
There was more involvement for our young players this afternoon as Fikayo Tomori made his full debut, and Billy Gilmour his first senior Chelsea appearance, off the bench.
Tomori was handed his first Chelsea start, and his second game in the league for us having appeared as a sub in May 2016. Andreas Christensen made way in what was the only change from the win at Norwich, and 18-year-old Gilmour was on the bench for the first time in a league game.
Chelsea yet again began brightly, zipping the ball around with plenty of confidence against energetic opposition. The first sight of goal was on five minutes when Emerson’s fine diagonal pass was controlled by the chest of Abraham, who was crowded out before he could shoot (pictured top).
Sheffield United’s innovative 3-5-2 system, involving overlapping centre-backs, has earned Chris Wilder and his team plenty of plaudits in the last 12 months. Lampard added his name to those heaping praise on them in his press conference yesterday, and from their early attacks it was clear the Blades’ greatest threat would come from out wide.
But as the boss had alluded to, that can leave space to exploit on the flanks and we did just in the 19th minute. Ross Barkley won a midfield battle and cutely backheeled to Christian Pulisic, who laid it out wide to Cesar Azpilicueta.
His cross was met by headed down by Abraham. Henderson couldn’t gather it under pressure from Pulisic, who had continued his run. The ball bounced back into Abraham’s path and he slammed home from eight yards out.
In search of a quick second, Ross Barkley drove forward with purpose but found his route to goal blocked. Down the other end, Chris Basham half-volleyed over after Zouma’s headed clearance sat up nicely for him.
Mateo Kovacic was enjoying another enterprising half in midfield and he nearly opened his Chelsea account after the half-hour. After slick interplay involving Pulisic and Abraham, the Croatian burst into the box and flashed a shot past the left-hand post.
Robinson then served a warning of his threat when he nodded wastefully wide from close range as Basham hooked a delivery into our six-yard box.
And Abraham punished that miss a couple of minutes before the interval. Two of the Blades’ centre-backs, John Egan and Jack O’Connell, got in a muddle dealing with a high Jorginho pass. Abraham was alert to the mistake and took a touch before firing past Henderson, who got a hand to the strike but was beaten for power.
Another searching Jorginho pass found Mount, who controlled delicately only to see Basham’s stretching leg divert his strike off target.
For the first time this season we had a two-goal lead, so that only made Sheffield United’s goal 45 seconds after the break all the more frustrating. Enda Stephens wriggled free down the left too easily and his centre was perfect for Robinson to sidefoot into the net from eight yards out with the visitors' first effort on target. 2-1.
Abraham thought he had his hat-trick 10 minutes later after superb work from Azpilicueta. He flicked the ball over a defender’s head and scooped in a cross that our striker turned on target. This time Henderson showed sufficient resistance, impressively palming the ball away.
Robinson went straight up the other end and shot wide, and then Barkley drew Henderson into a more comfortable save. It was his final contribution before Willian replaced him on the hour. Pulisic went wide left and Mount slotted inside.
With Sheffield tails up, Norwood tried his luck from range and Kepa gathered at the second attempt.
Seven minutes were left when Zouma headed a Mount corner over, and then Gilmour was introduced for his debut, replacing two-goal Tammy. Considering the match was still very much in the balance it was further evidence of Lampard’s faith in our youngsters. Michy Batshuayi was brought on for Kovacic at the same time, marking his first appearance of the season.
Mount nearly had a third goal in three games when Henderson punched a free-kick as far as him. His volley whistled agonisingly wide.
And then Tomori produced an outstanding block to stop sub Lys Mousset’s close-range strike, but the Blades did level with a couple of minutes left. Robinson’s cross from wide on the left was a superb one, and Zouma, under pressure from Mousset, was helpless to do anything but touch it into the far corner, where it was heading anyway.
It was an agonising moment. Four minutes of added time were played out with the Blues unable to break down the visitors' defence, meaning the celebrations at the final whistle were in the away end.
Chelsea (4-2-3-1): Kepa; Azpilicueta (c), Tomori, Zouma, Emerson; Jorginho, Kovacic (Batshuayi 83); Pulisic, Barkley (Willian 60), Mount; Abraham (Gilmour 84).
Unused subs Caballero, Christensen, Alonso, Giroud.
Scorer Abraham 19, 43
Sheffield United (3-5-2): Henderson; Basham (Osborn 84), Egan, O’Connell; Baldock, Lundstram, Norwood (c), Freeman (Mousset 78), Stevens; McBurnie (McGoldrick 63), Robinson.
Unused subs Moore, Stearman, Osborn, Besic, Sharp.
Scorers Robinson 46, Zouma own goal 89
Booked McBurnie 45
Referee Stuart Attwell