After Zlatan Ibrahimovic had given Sweden the lead in the 52nd minute, Shevchenko responded by heading in the equalizer just three minutes later and then added the winner in the 61st.
The victory gives Ukraine a serious chance of advancing from Group D after England and France drew 1-1, while Sweden faces an uphill battle to remain in the tournament.
Shevchenko is already a national icon in Ukraine and carried the hopes of the team going into the tournament. In front of sea of yellow and blue in the packed Olympic Stadium, he certainly didn't disappoint. He rewarded the faith coach Oleg Blokhin showed in the veteran.,
Showing flashes of the scorer's instinct that once made him one of the world's top strikers, Shevchenko beat Olof Mellberg to a cross for his first goal and then met a corner to head the ball inside the near post for the second.
That set off shouts of "Sheva" that could reverberate throughout the nation for a long time.
These days it's Ibrahimovic who is considered a world-class forward, but AC Milan's current star came up short against its former standout forward.
Ibrahimovic did provide the focal point of the Swedish attack and shaved the post with a header in the first half before putting his team ahead.
Kim Kallstrom collected a long cross at the left side of the penalty area and sent it to Ibrahimovic in front of the net. The Sweden striker calmly slotted the ball past Andriy Pyatov and into the net.
But Sweden seemed to relax after that and Shevchenko took advantage by meeting Oleh Gusev's cross and sending his header past Andreas Isaksson.
That made the home crowd erupt and the noise grew even louder six minutes later as the 35-year-old Shevchenko's header from a corner found its way past defender Mikael Lustig at the near post. That sent Blokhin jumping up and down the sideline and waving his hand frenetically.
Ibrahimovic had one good chance to equalize, but his hard, swerving shot was saved by Pyatov. Substitute Johan Elmander and Mellberg both shot high in the final minutes.
Shevchenko was given a well-deserved standing ovation as was taken off in the 81st, while Ibrahimovic strode off the field immediately after the final whistle with his head down.
