Victory in both their final Group Nine games - at home to Bosnia and Lithuania next month - will confirm Craig Brown's team as runners-up to the Czech Republic. One win might even be enough. But after this desperate struggle, against a nation with a negligible footballing pedigree, qualifying for the tournament in the Netherlands and Belgium might, once again, be as good as it gets.
Estonia set out to knock Scotland off their perch with the kind of gusto their countrymen brought to the task of toppling the nearby statue of Lenin after re-gaining independence. Had it not been for the agility of Neil Sullivan in Scotland's goal, they might well have claimed their most prestigious victims to date.
At the end, the Scots were booed off by many of their 1,000 supporters. To compound Brown's discomfort, the only caution of a physical contest was administered to Don Hutchison for taking a late free-kick too quickly. He will now be suspended for Bosnia's visit.
Perhaps no one, least of all the Scots, should have been unduly surprised by Estonia's vigour. They have come a long way since the Aberdeen crowd patronisingly clapped their consolation goal in 1993, their first in nine internationals. The possibility that they might take second spot themselves had clearly captured the public's imagination, and the small stands that were desolate when Scotland kicked off the three-second "game" of 1996 crackled with excitement throughout.
The home players were appropriately fired up, too, hustling Scotland out of their stride and biting in the tackle the way the Scots would do against one of the European superpowers. If some of their methods were crude or illegal, there was no doubting their effectiveness.
Aivar Anniste had a kick like Vana Tallinn, the sticky, cloying spirit with which the Tartan Army had no doubt acquainted themselves in the local hostelries. Sergei Hohlov-Simson stuck to the Scottish strikers like a skin graft, and only extreme leniency kept his name out of the referee's notebook.
One of Estonia's principal tactics was the booming long kick of the goalkeeper Mart Poom. Scotland dealt with it comfortably enough, but were often disconcerted by Andres Oper's willingness to chase any cause, however forlorn, and generally failed to impose their superior skills.
Some 26 minutes had elapsed before a clever pass by Martin Reim left Oper bearing down on Sullivan. To Scottish relief, the Wimbledon keeper bravely smothered the ball. It was stoppage time in the first half before Scotland retaliated. David Weir instigated the opening with a pass to Hutchison, whose flick played in Billy Dodds. From the angle of the six- yard area, Dodds took aim only to find Poom charging out to save with his feet.
Although the sun, which has blazed down on the capital all week, withdrew its favours in the second half, there was no sign of the controversial floodlights flickering into life or of any Uefa equivalent of Dicky Bird brandishing a light meter. However, the heat had taken a toll and the game began to open up.
What must have concerned Brown was that Estonia enjoyed the majority of the chances. Within eight minutes of sending on Indrek Zelinski - for whom Blackpool hope to secure a work permit tomorrow - the substitute and Oper combined to set up a free shot for Sergei Terehhov, who directed it straight at Sullivan.
Scotland's saviour promptly turned playmaker, launching the kind of long kick that is his club's trademark. Dodds, alighting on the ball six yards out, volleyed straight at Poom.
The respite was short-lived. No sooner had Sullivan dived to parry Reim's goalbound hook from 25 yards than Raio Piiroja's header was cleared off the line by John Collins.
Oper was transparently shattered but typified Estonia's work-rate by continuing to harass Colin Hendry and his cohorts into conceding corners. Zelinski headed one into the ground so hard that it reared over the top. Piiroja glanced another towards the far post, where Neil McCann emulated Collins' rescue act.
Scotland finished the stronger. Collins and Hutchison forced Poom to earn his corn, while the ball pinged around the Derby man's area as if in an arcade game on one occasion. A goal at that stage would have been as unfair on Estonia as it would have been kindly for Scotland.
ESTONIA (4-4-2): Poom (Derby); Kirs (Kotkan, Fin), Hohlov-Simson, Piiroja, Saviauk (all Flora Tallinn); Kristal, Anniste (both Flora), Reim (Kotkan), Terehhov (Flora); Oper (Aalborg, Den), O'Konnel Bronin (Levadia Maardu). Substitute: Zelinski (Flora) for O'Konnel Bronin, h-t.
SCOTLAND (3-5-2): Sullivan (Wimbledon); Weir (Everton), Hendry (Rangers), Dailly (Blackburn); Johnston (Sunderland), Burley (Celtic), Durrant (Kilmarnock), Collins (Everton), Davidson (Blackburn); Hutchison (Everton), Dodds (Dundee United). Substitutes: McCann (Rangers) for Johnston, 54; Ferguson (Rangers) for Durrant, 66.
Referee: F Stuchlik (Austria).
More football, pages 30-31