Chelsea scored three times in 11 second-half minutes to ease into the fourth round of the FA Cup with a 4-0 win over Preston at Stamford Bridge.

A frustrating showing from Mauricio Pochettino’s side, in which they hogged the ball throughout the first half but carved few openings, burst to life 13 minutes after the break with Armando Broja heading in his second goal of the season from Malo Gusto’s cross.

That was followed by two in rapid succession, first from substitute Thiago Silva, who nodded in from Cole Palmer’s corner, then another when Raheem Sterling whacked a free-kick beyond the dive of goalkeeper Freddie Woodman, as Preston’s accomplished first-half defensive showing faded into memory.

Enzo Fernandez tapped in right at the end from a yard out, a final reminder of the gulf to Ryan Lowe’s side who are 14th in the Championship.

Sterling had had the game’s first chance, shooting towards Woodman’s top corner after 17 minutes, his effort turned behind at the near post. Moments later Palmer should have opened the scoring when he beat the Preston offside trap from Mykhailo Mudryk’s lofted pass and tried to lift the ball into the goal, but saw his dinked attempt drop inches wide.

Preston contained Chelsea well for the opening half-hour and carved an opening of their own, Milutin Osmajic darting into the box from a headed flick-on and attempting a finish across Djordje Petrovic, though it was light work for the goalkeeper to drop to his right and save. Will Keane’s scuffed shot from the edge of the box was fielded with similar ease.

Fernandez might have done better when he flung his head at Sterling’s deflected cross, in the end an easy catch for Woodman as a frustrating first half stubbornly failed to ignite.

Pochettino named a near full-strength side, the only surprise a first senior start at right-back for academy graduate Alfie Gilchrist. The 20-year-old acquitted himself well, willing to show for the ball and a composed defensive presence, but his teammates on the whole delivered as drab and uninspiring a 45 minutes as home supporters have witnessed this season.

Much of Chelsea’s problem under Pochettino has stemmed from players being too static when in possession, rendering attacking moves easy to anticipate for opposition defenders. Here in the first half, Palmer and Fernandez showed themselves again to be excellent passers of the ball, but with too little movement the play became predictable.

It was not a surprise then that the opening goal came from a Preston mistake. Keane was caught in possession inside his own penalty area, and the lively Mudryk hounded him off the ball. He knocked it back to Gusto, who whipped in a superb cross met by the head of Broja, stealing in ahead of Liam Lindsay to glance it into the far corner to the home fans’ audible relief.

Broja might and perhaps ought to have made it two, meeting Mudryk’s ball in and directing a near identical header an inch over Woodman’s crossbar, as Chelsea finally asserted their superior class.

A second goal though was not long in coming. No sooner had Silva emerged from the bench to an uproarious ovation from around the ground than he headed in for 2-0, rising unchallenged to thump Palmer’s header in at the near post.

Sterling’s goal to make it three was a peach, curling a free-kick into the top corner after Palmer was felled on the edge of the box, before a ludicrously drawn out VAR check confirmed a fourth from Fernandez at the end.