"It was not only a beautiful goal, it was an important goal," Bergkamp said. "It think it was the best revenge."
Both teams made one change from Saturday's meeting. With Paul Bracewell still feeling the effects on his knee of the high challenge for which Bergkamp was sent off, last season's leading scorer, Craig Russell, came in. Arsenal, suffering a severe striker shortage with John Hartson joining Ian Wright under suspension, pressed 20-year-old Stephen Hughes into action in midfield.
From the opening, though, it was Sunderland who impressed. As early as the fifth minute, Russell nipped in behind Tony Adams and won a free-kick which bobbled its way to Andy Melville, only for Martin Keown to clear off his toe. A minute later, Adams had to resort to desperate measures to prevent Michael Bridges bursting into the area.
The Wearsiders' best chance of the first half came in the 22nd minute when Bridges intercepted Adams' back pass and sent Russell away. He failed, however, to get a clean strike and David Seaman remained unruffled.
At the other end Lionel Perez - the Frenchman whose inspired keeping at Highbury forced this replay - was again in top form. When Bergkamp flicked the ball over Melville, he raced out to meet the Dutchman's feet and from the following Paul Merson corner produced a punch of prodigious length to clear the danger.
Another raw Roker recruit, 21-year-old John Mullin, ensured Perez was not needed when, in the 28th minute, he made a superb tackle on Bergkamp, who had latched on to Hughes' pass in the area.
Considering these two teams' disciplinary record - seven booked on Saturday and three sent off in their three encounters so far this season - referee Steve Dunn had a surprisingly quiet night, and what action he did take was a little harsh. Keown was booked in the 41st minute for a seemingly innocent collision with Russell, and in the 48th minute Parlour's name was taken when Mullin fell over his foot.
Arsenal, after a terribly lacklustre first half, took the lead within 45 seconds of the restart. Bergkamp created his own space on the edge of the area with a clever drag-back. Five deft touches without a challenge took him within striking distance and he casually chipped a curler over Perez's head and into the top right-hand corner of the net.
Immaculately taken, it was his seventh goal of the season and within 15 minutes his side could have been four ahead. Bergkamp, all his flicks now working and his vision suddenly unblinkered, allowed Parlour in but Perez saved well.
Merson, also inspired by the goal, immediately whipped in a devastating cross which Nigel Winterburn stooped to head, again unchallenged, against the inside of the post.
The best chance in this spell, though, fell to David Platt. Merson pinpointed his run from midfield, but Perez advanced quickly from his line and kicked the shot away.
Arsenal were by now rampant and they clinched the tie in the 64th minute. Bergkamp sent Merson away down the right to the byline and his delicate chipped cross cleared the keeper and met the head of Hughes. Sprawling in at the far post, he scored his first senior goal.
Sunderland came within inches of a reply when Melville sneaked in between Seaman and Adams. He smuggled the ball inches wide of the post and with it went Sunderland's chances.
Sunderland (3-5-2): Perez; Hall, Melville, Ord; Kelly, Gray, Russell, Williams, Kubicki; Bridges (Smith, 57), Mullin (Aiston, 87). Substitute not used: Heckingbottom.
Arsenal (3-5-2): Seaman; Keown, Adams, Bould; Parlour, Hughes, Vieira, Platt, Winterburn; Merson, Bergkamp. Substitutes not used: Morrow, Shaw, Lukic (gk).
Referee: S Dunne (Bristol).