Donovan struck deep into injury time to rescue his side, who were on the verge of going out. Algeria stood firm for 92 minutes in the face of intense pressure but Donovan pounced on a loose ball to smash home and send USA's fans into raptures.
After the game, Donovan broke down in tears as he was mobbed by his team-mates. He said: "It's been a long journey these last four years and I'm shocked, and so proud of our guys. We kept going and we believed.
"People that know me closest know I've worked so hard for this moment. It's unbelievable. I know people back home will be watching - we're not done yet.
On his goal Donovan said: "They were pushing a lot to try and score and we had to take some risks. Our guys at the back did a great job. I got the ball, gave it to Jozy and made a run. The ball came to me and time kind of stopped and I couldn't miss from there."
USA will now face the runners-up in Group D after their late heroics. Ghana are currently top of the group but they face scond-placed Germany in Tuesday night's fixtures. Third-placed Serbia take on Australia.