Almost inevitably, Overmars played a pivotal role in Arsenal's victory, scoring their first goal and helping to make the second for Dennis Bergkamp before half-time. United again belied their modest standing in the First Division and deserved the riposte from Lee Morris which set up a lively final few minutes, but the holders moved without further alarms to a home quarter-final against Derby or Huddersfield.
For a contest billed as a grudge match, the evening finished with grudging mutual respect. Apart from a flurry of relatively innocuous fouls which saw United receive three yellow cards shortly before and after the interval, to be followed into the referee's notebook by Tony Adams, there was little of the unsporting behaviour with which Overmars had tarnished the first encounter.
On a night of lively chant and counter-chant from a near capacity, cut- price crowd, the Dutch winger bore the brunt of the United fans' ire. They booed his name beforehand and his first few touches, they were taunting the Arsenal supporters with "You only sing when you're cheating", when the players were suddenly milling round. For a moment, the scene was reminiscent of those which followed Overmars' ill-judged actions in the first match.
This time the stoppage was to allow treatment to Graham Stuart, who had to be substituted in only the fifth minute after a strong challenge by Ray Parlour. Undaunted, United carved out a fine opening six minutes later following a mazy right-wing run and measured pass by Shaun Derry. Marcelo slipped Adams in the six-yard box, but the Brazilian's composure was not of the kind one associates with his nationality and his shot sailed into the North Bank.
His profligacy was punished by Premiership class in the 15th minute. Bergkamp and Stephen Hughes combined to release Overmars to run at Alan Kelly, and there was no disputing the quality of the finishing as his low shot beat the goalkeeper for power and placement.
Bergkamp, the creative if goalless force behind last Saturday's 5-0 rout of Leicester, moved back to within one of his countryman's tally with his 10th goal of the season nine minutes before the break. Overmars initiated the move with a sweeping 50-yard pass from one flank to the other, where Parlour cut the ball back from the byline. Bergkamp dug his foot beneath the ball to chip it deftly over Kelly from level with the penalty spot.
United, who were especially well served by the enterprising Wayne Quinn, spurned a further opportunity early in the second half. Morris did well to get into a scoring position at the expense of Steve Bould, but hesitated with "only" David Seaman to beat and allowed Nigel Winterburn to clear.
The game had been largely malice-free to that point, yet it did not take a rocket scientist to work out that one of the Blades would exact some form of retribution on Overmars. Derry duly scythed into him and was booked, but Overmars left to a rapturous ovation from the home support when he was substituted with 15 minutes remaining.
"Brucie, Brucie, take 'em off", they crowed at Steve Bruce, the Blades' manager, to which the Bramall Lane 3,000 replied with righteous humour: "We're supposed to be at home".
Parlour, with a drive which stung Kelly's fingers, and Adams, failing by inches to convert a cross-cum-shot by the subdued Nicolas Anelka, might have added to the Double winners' lead, but United stuck gamely to their task.
A header over the bar from Marcelo had already threatened the United goal which finally arrived in the 86th minute when Morris scrambled the ball in from close range. "It shows that you can have fair play and win," Arsene Wenger said. This time Bruce was in no mood to argue.
Arsenal (4-4-2): Seaman; Vivas, Adams, Bould, Winterburn; Parlour, Vieira, Hughes, Overmars (Garde, 75); Anelka (Kanu, 70), Bergkamp (Diawara, 80). Substitutes not used: Grimandi, Garde, Manninger (gk).
Sheffield United (4-4-2): Kelly; Derry, Holdsworth, Sandford, Quinn; Devlin (Twiss, 66), Hamilton, Woodhouse, Morris; Marcelo Stuart (Ford, 5). Substitutes not used: Henry, Jacobson, Tracey (gk).
Referee: P James (Loughborough).