Scotland led 2-0, and deservedly so, through goals by the former Hearts Boys' Club colleagues Paul Ritchie and Allan Johnston. If they had held firm for the next 10 minutes, a famous win to set above even the recent friendly success in Germany would surely have been theirs.
Instead, the Czechs halved the deficit almost immediately through Tomas Repka. Then, following a double substitution, one of the replacements, Pavel Kuka, hauled them level.
Scottish thoughts had already turned from a stunning victory to an honourable draw. With only four minutes left the other substitute, Jan Koller, struck to send the Czechs through to next summer's extravaganza, and all that was left was sickening defeat.
The Scots are rightly disdainful of their time-honoured role as plucky failures. Yet while their makeshift line-up could not quite become the first to take a point from the section leaders, there was much in the performance to encourage the belief that they are capable of at least qualifying for a play-off as runners-up.
For more than an hour, Brown's strategy worked better than he could have imagined. Colin Calderwood shackled Patrik Berger; Karel Poborsky produced more petulance than pace; the Liverpool-bound Vladimir Smicer became so exasperated that he hoofed the ball into the stand after being penalised, and was duly cautioned; while the towering Vratislav Lokvenc looked no more than a poor man's Niall Quinn.
Scotland's enterprise might have been rewarded as early as the 10th minute only for Ritchie, making his competitive debut, to head over following Ian Durrant's free kick. Billy Dodds also stung Pavel Srnicek's fingers with a low drive.
At the other end Neil Sullivan appeared intent on putting an uncertain display in the Faroe Islands behind him, saving well from Lokvenc after Pavel Nedved had dispossessed Paul Lambert. Suitably heartened, the Scots went ahead on the half hour.
Ritchie, over whose relative lack of height Brown had expressed misgivings, was granted a second free header from Callum Davidson's in-swinging corner. This time, the 23-year-old defender made no mistake.
The Czechs, perhaps caught up in the premature triumphalism of their supporters to that point, retaliated menacingly. A free-kick routine led to a drive by Nedved which Sullivan pushed behind at full stretch. When Repka applied a glancing header to the corner, the keeper saved well.
Having withstood the home team's initial flurry after the interval, Scotland doubled their advantage in the 62nd minute. The build-up was a model of teamwork and patience, Dodds taking a throw-in from Davidson before switching the ball to Kevin Gallacher, who delivered a low cross. Johnston, stealing in front of Srnicek, claimed his second goal in successive internationals with the deftest of near-post headers.
This affront to Czech pride finally stirred Jozef Chovanec's side. Within three minutes Repka met another corner from Nedved, but this time his header squeezed past Sullivan.
A double substitution, involving the arrival of Kuka and Koller, gave the Czechs further impetus and pushed the Scots on to ever deeper defence. With 15 minutes left, Smicer sent Kuka scampering clear of David Weir to loft the ball over the onrushing Sullivan.
Koller, even taller than Lokvenc but far more effective on the ground, finally found space in the Scottish six-yard box to head in from Berger's free-kick. Czech rapture was tinged with relief. Scotland, not for the first time, deserved better.
CZECH REPUBLIC (3-5-2): Srnicek (Sheffield Wednesday); Repka (Fiorentina), Hornak (Sparta Prague), Suchoparek (Strasbourg); Poborsky (Benfica), Hasek (Sparta Prague), Nemec (Schalke 04), Nedved (Lazio), Berger (Liverpool); Smicer (Lens), Lokvenc (Sparta Prague). Substitutes: Baranek (Sparta Prague) for Hasek, 61; Kuka (Nuremberg) for Poborsky, 69; Koller (Lokeren) for Lokvenc, 69.
SCOTLAND (3-5-2): Sullivan (Wimbledon); Boyd (Celtic), Weir (Everton), Ritchie (Hearts); Johnston (Sunderland), Durrant (Kilmarnock), Calderwood (Aston Villa), Lambert (Celtic), Davidson (Blackburn); Gallacher (Blackburn), Dodds (Dundee United). Substitute: Jess (Aberdeen) for Durrant, 71.
Referee: H Krug (Germany).