Last-gasp penalty save secures Germany women's bronze medal against Spain
Giulia Gwinn converted a 65th-minute penalty in Lyon to give Germany the lead but Spain had the chance to force extra time when they won a spot-kick of their own right at the end of seven minutes of injury time.
However, former Ballon d'Or winner Putellas had her effort from the spot saved by the heroic Berger as Spain missed out on a medal on their debut appearance at the Olympics.
Berger had already been the star for Germany in the quarter-final win against reigning champions Canada when she saved two penalties in a shoot-out before converting the decisive kick herself.
It is the fourth time Germany have taken Olympic women's football bronze after 2000, 2004 and 2008. They won the gold medal in 2016, while coach Horst Hrubesch was also in charge of the men's team that won silver at Rio 2016.
Meanwhile, the defeat confirms a disappointing end to the tournament for Spain, who had come to their debut Olympics among the favourites for a medal on the back of their run to World Cup glory a year ago.
Led by reigning Ballon d'Or Aitana Bonmati, they underlined that status by completing the group stage with a 100 per cent record, but then had to come back from two goals down against Colombia in the quarter-finals before eventually going through on penalties.
Their hopes of gold went up in smoke in a 4-2 defeat by Brazil in the semi-finals, setting up a play-off for bronze with a German team that lost in extra time to the United States in the last four.
Germany won a penalty just after the hour mark when Gwinn was clattered into by Spain goalkeeper Cata Coll just inside the box.
Gwinn stepped up to stroke in the spot-kick, and that looked to be that with Spain rarely seriously threatening Berger at the other end.
But then they were awarded a penalty of their own when Lucia Garcia was clipped in the area by Janina Minge.
With the game into its 99th minute, Putellas stepped up and struck the kick firmly, but Berger flew to her left to keep it out.
The USA face Brazil in the gold medal match in Paris on Saturday.