Leeds beat Accrington Stanley 3-1 to book their place in the fifth round of the FA Cup for the first time in seven years as Leicester also avoided a shock with a 1-0 win at Walsall on Saturday.
Jack Harrison's stunning long-range strike settled Leeds' nerves of an upset against the League One side at the Wham Stadium.
Jesse Marsch's men face a fight to survive in the Premier League, but are beginning to click as an attacking force with the return of Patrick Bamford and Luis Sinisterra from injury to complement new signing Georginio Rutter.
Bamford's brilliant reverse pass teed up Junior Firpo to double the visitors' lead just after the hour mark.
Two minutes later, Sinisterra tapped home Harrison's cross to end the tie as a contest.
But there was a moment to savour for Stanley as 18-year-old Leslie Adekoya pulled a goal back nine minutes from time.
Leicester were pushed even closer by League Two Walsall only to be bailed out by FA Cup specialist Kelechi Iheanacho.
The Nigerian has scored more goals in the competition than any other player since making his debut in 2016.
Iheanacho's 17th goal in 23 FA Cup appearances had some fortune as his strike from the edge of the box took a wicked deflection for the only goal 23 minutes from time.
Leeds and Leicester join Manchester City as the first three sides to book their place in the last 16 of the cup.
City saw off Arsenal 1-0 on Friday night in a clash between the top two in the Premier League.
Harry Kane can move out on his own as Tottenham's all-time top goalscorer later on Saturday when Spurs visit Preston.
Manchester United are also in action against Championship opposition as Erik ten Hag's men host Reading.