Reid's side snatch shoot-out victory.
11th November 1998
Everton 1 Sunderland 1 (aet, 4-5 on pens)
Sunderland were last victorious at Goodison Park in November 1998 with a League Cup win over the Toffees, after they put to bed spot-kick misery at Wembley the previous May with a 4-5 win on penalties.
Peter Reid was missing a handful of first-team regulars, including Kevin Phillips, Danny Dichio, Kevin Ball, Nicky Summerbee, Michael Gray and Alex Rae for the cup tie, but Sunderland still managed to push their top-flight opposition to the limit.
Both sides rarely threatened in the early stages, Niall Quinn was denied when clean through after Craig Short's last-ditch interception and Duncan Ferguson headed the ball straight into Thomas Sorensen's hands from close range.
The Black Cats moved into the lead just before the half-hour mark, as Sorensen's long clearance flew over the heads of the Blues defence and Michael Bridges raced clear before coolly slotting the ball past Everton keeper Thomas Myhre.
Sunderland took charge after going in front and the striker could have doubled his side's lead minutes later but shot tamely at Myhre.
John Collins came to Everton's rescue on 74 minutes, after converting a free-kick that was rewarded after Darren Williams upended Ibrahima Bakayoko.
Everton moved up a gear after Collins' lifeline but still didn't do enough to see off Sunderland as the tie went to extra time.
The hosts had a double let-off on 102 minutes, as young substitute Michael Proctor had a shot parried by Myhre before blazing the rebound over the crossbar.
Neither side could find a winner, and so the game was to be decided on the lottery of penalties.
Martin Scott gave the visitors the lead with the first penalty, before Michael Ball levelled matters for Everton.
Allan Johnston restored Sunderland's advantage, but Collins also hit the target.
Martin Smith scored, before centre-half Marco Materazzi showed a level head as he sent Sorensen the wrong way.
Chris Makin hit the top of the crossbar with the seventh penalty, followed by John Oster who wasted the chance to give Everton the lead, sending his shot high and wide.
Lee Clark, making his first appearance since breaking his leg earlier in the season, scored, but Tony Grant sent the shoot-out into sudden death.
Quinn also hit the target, before Bakayoko sent his side crashing out of the League Cup at the hands of lower division opposition for the fourth times in five seasons.
Sunderland were headed for a home tie with Luton Town in the fourth round of the competition. That season Peter Reid steered his all-conquering side to the semi-finals of the competition as well as the Division One Championship.
Everton: Myhre, Short, Ball, Dacourt (Cleland 45), Materazzi, Bakayoko, Collins, Dunne, Ferguson, Hutchison (Oster 66), Cadamarteri (Grant 66)
Sunderland: Sorensen, Makin, Scott, Thirlwell (Clark 73), Melville, Butler (Craddock 48), Smith, Williams, Quinn, Bridges (Proctor 61), Johnston