Enzo Le Fee's first-half volley looked to have secured Sunderland's place in the draw, but James Garner sent the tie to extra-time with his 89th-minute penalty.

However, the midfielder could not replicate his successful spot-kick in the shootout, with Roefs denying Garner, Thierno Barry and Beto to get the Black Cats over the line at Hill Dickinson Stadium.

Both Noah Sadiki and Simon Adingra had shots blocked early on, while 18-year-old Harrsion Armstrong saw a half-volley from the edge of the box fly narrowly over Roefs' goal after Sunderland struggled to clear its lines.

The breakthrough then came in the 30th minute. The Toffees failed to deal with a long throw that found its way to Eliezer Mayenda, who teed up Le Fee for a first-time effort which nestled in the bottom-right corner.

Vitalii Mykolenko went close either side of the break for Everton as it searched for an equaliser, with Dwight McNeil firing over from distance as it found it difficult to play through Sunderland's resolute defence.

The visitors looked comfortable with their one-goal advantage, but Adam Aznou caught Nordi Mukiele dwelling on the ball in the box before drawing a foul from Trey Hume, and Garner sent the game to extra time by sending Roefs the wrong way from the spot.

After neither side found a winner in the additional 30 minutes, Roefs produced his heroics, with Le Fee, Granit Xhaka and Luke O'Nien all scoring for Sunderland as it won 3-0 in the shootout.