Mario Pasalic had a glorious opportunity to stun The Kop in the third minute as he drew a wonderful, sprawling save from Kelleher, but the floodgates opened in the 38th minute.
Aguero had a glorious chance to make it 2-0 from the spot moments later when Billy Gilmour fouled Gabriel Jesus, but the Argentina striker opted for a dinked effort that was easily saved by Edouard Mendy.
In the week in which a Mason Mount mural was unveiled off the Fulham Road outside Stamford Bridge, the young midfielder produced some artistry of his own to tee up Hudson-Odoi with a glorious pass from inside his own half and the forward did
Antoine Griezmann hit the bar for Barca from a tight angle and missed a glorious chance when he tried to slide the ball into an empty net but deflected it to the keeper.
Much of the pre-match talk from the Manchester City camp revolved around the desire to give Pellegrini a glorious send-off following confirmation that Bayern Munich coach Pep Guardiola will take his job from next season.
John Fleck missed a glorious chance to make it 2-0, which proved costly as Ole Gunnar Solskjaer's side dominated thereafter against the winless Blades.
The home side were less effective following the interval but McTominay (69) restored their advantage with a close-range header from Alejandro Garnacho's cross, before the Argentine wasted a glorious opportunity to wrap up victory on the break
In an encounter that rarely hit the heights despite lots of effort, Arsenal - who had seen a penalty over-turned by the VAR after referee Anthony Taylor originally ruled Havertz had been fouled - missed a glorious late opportunity when Bukayo