While the Third Division club converted all five of their spot-kicks, a miss by the Conference side's midfielder Steve Taylor proved crucial. Plymouth now visit Wycombe in the second round on Saturday.
Graham Allner, Kidderminster's manager, was in the Worcester line-up which knocked out Malcolm Allison's Plymouth in 1978, still their only defeat by non-League opposition. He must have been surprised by his team's strangely passionless display prior to extra time.
If ever a League team were ripe for a giant-killing, it was Plymouth. Ravaged by injuries, they gave a debut to a 16-year-old Youth Training Scheme boy, Darren Bastow, fielded two full-backs with barely a dozen appearances between them and even had Kevin Hodges, their manager, on the bench six years after he last played for the club.
Yet they almost claimed the first goal in more than two hours of the tie with just four minutes played. Kidderminster cleared a corner straight to Martin Barlow, whose 18-yard volley was diverted on to a post by his team-mate Earl Jean.
Jean's pace and willingness to pursue forlorn causes gave Plymouth a cutting edge which Kidderminster lacked. Both the St Lucian and Chris Hargreaves forced agile saves from Stuart Brock either side of the part- timers' only real moment of menace before half-time, when Stewart Hadley's goal-bound volley cannoned to safety off Mick Heathcote.
As if Plymouth's personnel problems were not serious enough they lost two players in 10 minutes before half-time. Steve McCall had to be carried off after a reckless tackle by Mark Yates, soon to be followed by the limping Hargreaves.
The closing moments before the break exemplified the difference in the sides' attacking capabilities. An overhead kick by Kidderminster's Leroy May reached Jon Sheffield in instalments, whereas Brock kept out a Sean McCarthy header with great difficulty.
Kidderminster at last played with a modicum of conviction in the second half. However, 67 minutes had elapsed before Taylor tested Sheffield's athleticism, and the form which swept the Harriers of '94 past Birmingham and Preston en route to a fifth-round exit against West Ham was largely absent.
In the additional half hour, Lee Phillips put the ball wide after rounding Brock, while Yates headed against the bar. With 70 seconds remaining, Sheffield clawed out Taylor's long-range effort; the Kidderminster player's aim was to prove less reliable from 12 yards.
Kidderminster Harriers (4-3-1-2): Brock; Hinton, Smith, Webb, Hines; Cunnington (Willetts, 71), Yates, Taylor; Arnold; May, Hadley (Deakin, 91). Substitutes not used: Bignall, Wolsey, Acton (gk).
Plymouth Argyle (4-4-2): Sheffield; Ashton, Heathcote, Wootton, Beswetherick; Bastow, McCall (Sweeney, 35), Barlow, Hargreaves (Phillips, 44); Jean, McCarthy. Substitutes not used: Hodges, Adams, Dungey (gk).
Referee: A Butler (Sutton-in-Ashfield).Reuse content