On an afternoon when both sets of players put their followers through a maelstrom of emotions, Hewitt's header provided the final, dramatic twist. But if the town of the crooked spire will spend another eight days in dreamland, praying for the great old competition to provide one more example of its wonderfully warped logic and send a Second Division club to Wembley for the first time, a draw was the last result Boro wanted.
Already facing one replay in Sheffield, against Leicester on Wednesday, Bryan Robson's men must now find a fresh date for the Premiership game at Tottenham that was scheduled for the following night. Given that they have yet to agree a slot for the visit to Blackburn, they appear certain to end the season striving to stave off relegation amid a flurry of fixtures.
They will receive scant sympathy from Chesterfield. John Duncan's gallant team, having had a third "goal" dubiously disallowed when they led 2-1 with 21 minutes of normal time left, can legitimately argue that they might have been in an unassailable position against a side reduced to 10 men by the dismissal of Vladimir Kinder shortly before half-time.
Television replays supported Duncan's contention that Jonathan Howard's shot against the bar had come down over the line, but it would have been a travesty if Boro's diminutive Brazilian, Juninho, had finished a loser. For much of the first half he was dogged by Chesterfield's Mark Jules with the tenacity of Christine Hamilton pursuing Martin Bell.
But as the Teessiders' plight worsened, Juninho drew on his reserves of incendiary energy to haul them back into contention. Within a minute of their reprieve from referee David Elleray, he earned Boro the second penalty of the match and extra time.
Heartbroken as Boro were when Hewitt cancelled out Gianluca Festa's strike early in the additional half-hour, football had been the winner. Even at the theatre of dreams, encounters as exciting and unpredictable as this come around about as often as the Hale-Bopp comet.
Yet until Kinder's 37th-minute exit, for tugging the shirt of the massively impressive Kevin Davies and incurring his second yellow card, Boro had enjoyed the upper hand. Chris Perkins hacked a Mikkel Beck header off the line; Juninho fired over after a rare lapse by Sean Dyche; and Billy Mercer upheld the grand tradition of Chesterfield goalkeepers with a fine save from Craig Hignett.
Offered the initiative by the Slovakian's stupidity, Chesterfield seized it with both hands. Howard had already volleyed over with only Ben Roberts to beat before redeeming himself nine minutes after the interval. Following neat interplay between Howard and Davies, the ball was drilled low across the six-yard box. Roberts parried, but Andy Morris was able to walk the rebound in from point-blank range.
On the hour, the giant Morris left Festa trailing as they chased a through ball and rounded Roberts before being toppled by the keeper. Dyche, whose previous claim to fame was that he used to do Brian Clough's gardening during his days as a reserve at Nottingham Forest, bludgeoned the spot- kick past Roberts.
For four minutes Wembley looked certain to be accommodating CFC fans on all four sides on 17 May. Then Emerson fed Clayton Blackmore, and the former Manchester United player's cross was bundled in by Fabrizio Ravanelli.
Chesterfield were still pondering how Mr Elleray had managed to rule out Howard's Geoff Hurst impersonation when Boro charged upfield to draw level. Dyche bowled over Juninho, and though the offence was clearly obstruction and took place just outside the area, Hignett buried the penalty beneath Mercer.
Two decisions in two minutes and the referee had called both wrong. To Chesterfield's further chagrin, Boro proceeded to make light of their numerical disadvantage in extra time.
Ravanelli, with a neat pass, supplied Robbie Mustoe with a shooting chance which he sent against the bar. Festa, the former Internazionale defender, was perfectly if mysteriously placed to shoot Boro ahead for the first time.
Chesterfield's 23,000 supporters had begun a rather mournful chorus of "We're proud of you" when Chris Beaumont crossed hopefully from the right. As the ball landed, it reared up obligingly for Hewitt to power only his second goal of the season out of Roberts' reach.
They thought it was all over, to paraphrase the title of the TV show on which the pounds 320,000 team appeared last week, but it is not yet.
Goals: Morris (54) 1-0; Dyche (pen, 60) 2-0; Ravanelli (64) 2- 1; Hignett (pen, 70) 2-2; Festa (100) 2-3; Hewitt (119) 3-3.
Chesterfield (4-4-2): Mercer; Hewitt, Williams, Dyche, Jules; Howard, Curtis, Holland (Beaumont, 75), Perkins (Carr, 84); Morris, Davies. Substitute not used: Leaning (gk).
Middlesbrough (4-3-2-1): Roberts; Fleming, Festa, Vickers, Kinder; Hignett (Moore, 117), Emerson, Mustoe; Juninho, Beck (Blackmore, 39); Ravanelli. Substitute not used: Whyte.
Referee: D Elleray (Harrow-on-the-Hill). Bookings: Chesterfield: Curtis, Jules, Dyche. Middlesbrough: Kinder, Blackmore, Roberts. Sending-off: Kinder.
Man of the match: Juninho. Attendance: 49,640.