Early goals from Kenny Miller and Lee McCulloch put the Scots on the road to a Group B victory over last year's FIFA World Cup™ quarter-finalists. Although Chelsea's Andriy Shevchenko gave Ukraine hope by pulling one back before the break, James McFadden made sure Scotland would take all three points with a third goal in the second half.
Alex McLeish's side lead the table, ahead of both Italy and France, with only two games remaining, away to Georgia on Wednesday and at home to Italy next month.
Scotland had given themselves the perfect start with the opener in only the fourth minute. Scott Brown was fouled on the touchline by Andriy Nesmachny and McFadden, scorer of Scotland's sensational winner in France last month, took the free-kick, swinging the ball in towards the front post, where Miller had raced in front of his marker to nod the ball home.
Ukraine tried to hit back quickly and in the ninth minute Oleh Gusev cut in from the right to blast an effort from 16 yards, which was deflected just over.
But Scotland, roared on by a capacity crowd at Hampden Park, doubled their lead in the tenth minute - again from a free-kick. Miller was fouled and this time captain Barry Ferguson chipped the ball to the back post, where McCulloch had cleverly found space. The Rangers midfielder had time to control the ball then curl it into the top corner of the net from 12 yards, beyond the despairing dive of goalkeeper Oleksandr Shovkovskiy.
Ukraine were on the ropes at this stage and Scotland continued to press forward looking to put the game beyond their reach. The home team had a claim when Alan Hutton went down in the penalty area, but referee Vink waved away the appeals from the Scottish players and fans.
However, in the 24th minute the visitors halved the deficit, when Nesmachny's cross deflected off Scotland defender Gary Naysmith and Shevchenko was perfectly placed to blast the ball into the roof of the net from six yards.
The game was now evenly balanced with both sides rushing forward when in possession, and this continued into the second half. Ukraine had the first effort on goal in the second period when Liverpool's Andriy Voronin's long-range shot flew a few feet wide in the 49th minute.
Two minutes later Voronin forced Scotland goalkeeper Craig Gordon into action for the first time in the match, with a low drive from 20 yards which required the Sunderland stopper to dive to his left to palm away. In the 67th minute, at the other end, Miller's first time shot from 25 yards was easily gathered by Shovkovskiy.
But in the 68th minute Scotland restored their two goal advantage. Hutton spotted McFadden's run and played a perfectly weighted pass to the Everton forward, who controlled the ball before smashing it low past Shovkovskiy from 12 yards to seal another superb victory for McLeish's side.