The victory at Stamford Bridge extended Chelsea manager Thomas Tuchel’s unbeaten start in London – the German has now won 10 matches and drawn four in all competitions since replacing Frank Lampard in January.
Chelsea have moved into contention for a top-four finish in the Premier League and reached the Champions League quarter-finals, but Tuchel said he witnessed a tired performance from his team on Sunday.
Sheffield United, bottom of the Premier League, showed early attacking intent but fell behind in the 24th minute when Norwood steered the ball into his own net as he attempted to block Ben Chilwell’s shot.
With the Blades throwing men forward in the dying seconds, Ziyech produced a fine finish after a quick counter-attack to seal Chelsea’s win in added time.
Chelsea could have scored another through Christian Pulisic, but the American forward lost his footing and his shot was blocked by Aaron Ramsdale.
Sheffield United were rejuvenated after the break, but lacked the killer instinct in front of goal and squandered a couple of clear chances.
The FA Cup semi-finals take place in April, with the final on May 15.
