Craig Levein’s men, who saw Darren Fletcher miss a penalty, hung on in a nervous finale for only their second victory of the campaign.
Naismith (right) scored just after the break when he stretched to meet a whipped cross from the outstanding Barry Bannan with a half-volley that went in via the post.
It means Scotland lie two points behind the Czech Republic in a two-way fight for second place, with two fixtures remaining. Group I leaders Spain confirmed their qualification with a 6-0 win over Liechtenstein. Elsewhere, the Republic of Ireland secured a vital draw in Russia with a heroic rearguard effort that left defender Richard Dunne covered in blood and wearing a shirt with his number scrawled on the back in marker pen.
Dunne made several crucial blocks and goalkeeper Shay Given a string of superb saves to earn a seventh consecutive clean sheet and stay just two points behind the Group B leaders.
A facial wound forced the Aston Villa centre-back to change his shirt, but with only blanks in their kit bag Irish staff had to add a makeshift No5 to Dunne’s new top with a pen. Qualification rivals Slovakia, meanwhile, suffered a huge shock 4-0 home defeat to Armenia, keeping them one point behind Giovanni Trapattoni’s men, and with Russia still to play. Ireland face easier final matches against Andorra, away, and Armenia, at home, next month.
Northern Ireland’s hopes of reaching the finals died as they lost 4-1 in Estonia. Group C leaders Italy confirmed top spot by beating Slovenia 1-0. World No1 ranked side Holland also booked their Euro 2012 spot with a 2-0 win in Finland.