Roman Pavlyuchenko scored in the 24th minute, for his second of the tournament, and Russian player of the year Andrei Arshavin added a second in the 50th minute to seal victory.
Russia progress to their first ever knockout stages of a major tournament since the break up of the Soviet Union in 1991 and will play Holland in the quarter-final in Basel, Switzerland, on Saturday - a repeat to a certain extent of the 1988 final when present Dutch coach Marco van Basten scored in the 2-0 victory over the Soviets.
Russia are also coached by Dutchman Guus Hiddink, who took the Dutch to the 1998 World Cup semi-finals.
Swedish coach Lars Lagerbäck was gracious in defeat.
"I would like to congratulate the Russians, who really play joyful football," said the soon to be 60-year-old veteran handler.
"I think they saw rapidly where they could hurt us and they exploited our weaknesses perfectly."
Russia produced their usual flowing football in the early stages with playmaker Arshavin - coming back after a two match suspension - pulling the strings, and the unimaginative Swedes, who did start with star striker Zlatan Irahimovic despite his knee problem, content to sit back on the whole.
It was the Russians who went closest to opening the scoring in the 20th minute as Yuri Zhirkov unleashed a fierce volley from the left side of the penalty box which just crept past the far post of the Swedes, Arshavin having provoked the corner with a cheeky chip which forced Andreas Isaakson into a tip over.
However, they got a deserved lead in the 24th minute as Pavlyuchenko tucked away a finely made goal for his second of the tournament, having been set up by Zenit St-Petersburg's rampaging fullback Alexander Anyukov.
The Swedes hit back almost immediately as veteran striker Henrik Larsson got on the end of a long ball and his header clipped the bar much to the relief of Russian goalkeeper Igor Akinfeev.
The Russians were just playing the most delightful football, some of the best of the tournament, and in the 36th minute they went desperately close to doubling their lead as the redoubtable Pavlyuchenko was fed inside the box and his chip beat Isaakson only to clip the post.
The ball was crossed in again and Zhirkov fired fiercely on target only for Isaakson to produce a marvellous tip away save to leave it at that point the Russians having had 13 shots to the Swedes three.
Sweden, though, could not be discounted and captain Freddie Ljungberg forced Akineev into a scrambled save in the 44th minute but the Swedes failed to take advantage of the corner.
The Russians at last made their overwhelming superiority tell in the 50th minute as Arshavin scored their second, the 'little jewel' as he is fondly called, sliding the ball home after another glorious team move with the Zenit St Petersburg star at the end of Zhirkov's pass.
The Swedes were pretty toothless up front with Ibrahimovic clearly labouring and it was the Russians who should have gone 3-0 up 10 minutes from time as Konstantin Zyryanov's shot was deflected onto the post and thence to safety.
Then, as the Swedes pressed forward in desperate search of a goal - Lagerbäck having sent on veteran 35-year-old striker Marcus Allback in place of a defender - Pavlyuchenko had two glorious chances to add to the Russian tally but first miskicked and then seconds later directed his header into Isaakson's welcoming hands.
However, for the Swedes there was nothing welcoming about the final result.