Chelsea survived an FA Cup scare as Conor Gallagher came off the bench to score a last-minute winner and seal a 3-2 victory over Leeds at Stamford Bridge.

The substitute lashed the ball past the visitors’ goalkeeper Illan Meslier to grab what had looked an unlikely victory for much of the game, never more so than when the Blues fell behind inside eight minutes to the first of two goals from Mateo Joseph.

Mauricio Pochettino’s side rallied and looked to have put their woeful start behind them when first Nicolas Jackson and then Mykhailo Mudryk netted to send them in 2-1 up at the break.

Leeds would not lie down easy though, and Joseph headed them level after evading Trevoh Chalobah at the far post on the hour mark.

The home support bubbled with disquiet, sensing another cup mishap after Sunday’s Carabao Cup final loss to Liverpool.

Then came Gallagher’s late intervention to keep hopes of a Wembley return in May alive.

The opening 10 minutes were dominated by Leeds. They might have taken the lead when Daniel James found space on the edge of the box and acrobatically lobbed an effort wide.

It was a let-off for Chelsea, but they did not heed their good fortune. From the goal-kick, Axel Disasi played a short pass inside the penalty area that left Moises Caicedo vulnerable. Leeds snapped at his heels, dispossessing him, and the ball broke to Joseph, who cracked it past Robert Sanchez as Chelsea’s defence pointed fingers.

The first mutterings of discontent among the home support started, but they were doused before they had time to take hold. Caicedo made partial amends for his earlier error, sliding a precise ball through that split Leeds’ defence. Into the space strode Jackson, and he placed it into Meslier’s bottom corner to ease Chelsea nerves.

Thereafter they settled, and deservedly took the lead after 37 minutes. Noni Madueke carried the ball up through midfield and poked it to Malo Gusto wide on the right. He fed Raheem Sterling, who crossed for Mudryk to cap the move with a delightful finish, glancing it with a deft right foot wide of the goalkeeper and in.

James skied one over the bar from six yards as Leeds threatened an instant reply. Jaidon Anthony went closer when he curled wide from outside the box, a reminder that a stiff challenge might await Chelsea in the second half.

Daniel Farke’s team had won nine in a row in the league. Here they went up against Premier League opponents with the courage and skill to suggest they would fare well should they return to the top flight, but their hosts were giving ample encouragement.

The equaliser was straight forward and entirely avoidable from Chelsea’s point of view. Anthony was given space on the right to assess options and size up a cross. Stealing away at the far post was Jospeh, and his marker Chalobah paid him little heed as he stepped outside the defender and nodded past an exposed Sanchez.

The murmurs of disapproval began again from the stands, though they were largely drowned out by the away fans’ vocal support. They deserved better than the heartbreak that came as the clock ticked over to 90 minutes.

Enzo Fernandez was the architect of the winner, darting infield and through the heart of the defence and finally finding the pass that Chelsea had craved throughout the half. Gallagher, with fresh legs from the bench, let the ball run across him and with a swing of his right boot lashed Chelsea into the quarter-finals.