Germany won their first ever Olympic gold medal in women’s football on Friday when they turned in a superior second-half performance to beat Sweden 2-1 at the Maracana stadium in Rio de Janeiro.

The Germans, ranked No2 in the world, scored twice in the second half, and although the Swedes got a goal back they could not snatch an equaliser that would have taken the game into extra time.

The win meant Germany went unbeaten in the tournament and lifted them into an elite group alongside the United States and Norway as the only teams to win both the Women’s World Cup and the Olympics. Germany failed to qualify for the Olympics in 2012 but won the bronze the last three times they played, in 2000, 2004 and 2008.

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“This is something completely new, so this is definitely a new summit for German women’s football,” said German coach Silvia Neid, who is retiring after the Olympics. “I really don’t have words to describe this, it doesn’t matter if it’s the World Cup or Euros, this is what you have earned through your hard work over weeks and months. It’s really crazy when you get to the end. When you have finally reached your goal it is pure joy.”

Sweden, who scored just three goals in their five games before the final, started surprisingly positively but Germany began to impose themselves as the match went on and the best chance of the half fell to Anja Mittag after 25 minutes. Leonie Maier’s curling shot was only parried by the Swedish keeper and the ball fell to Mittag just yards from goal but she blasted the ball high and wide.

The sides were evenly match but things changed in the second half and it was the Germans who deservedly took the lead three minutes into the second period. When they did it was a goal worthy of a cup final. Dzsenifer Maroszan gathered a cross on the edge of the box and had time to steady herself before curling a perfect strike into the top right-hand corner of the net.

They extended their lead 14 minutes later thanks to an unfortunate own goal. A Sara Daebritz free kick from 20 yards smacked the post and Linda Sembrandt tried to clear but instead kneed the ball into her own goal from just a few yards out.

Sweden reacted almost immediately and just five minutes later Stina Blackstenius pulled them back into the game. Olivia Schough hit an inviting low cross into the box from the right and Blackstenius slid in between two defenders and poked the ball home to cut the deficit.

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Schough had a great chance to level the scores three minutes from time but her shot was blocked just yards from goal, much to the chagrin of a Brazilian crowd who were supporting the Swedes, perhaps because the German men’s side hammered Brazil’s men 7-1 in the World Cup two years ago.

“You just have to look back and be proud then it’s easier to get a smile on your face,” Swedish coach Pia Sundhage said of her unfancied team afterwards. “I think we should all be proud of what we have done and how we played.”