Frankfurt, already champions in 2002, 2006 and 2008 and finalists in 2004 and 2012, are now the most decorated European club ahead of Wolfsburg, Potsdam, Umea and Lyon, who have two each.
But if the team of striker Celia Sasic, by far the top scorer in the tournament with 14 goals this season, crushed all their rivals with 40 goals for just two conceded in eight matches, they had to battle past the French novices.
The Ligue 1 runners-up, who had eliminated French champions Lyon and two-time defending champions Wolfsburg en route to the final, held firm for the first 30 minutes largely thanks to the efforts of their Polish goalkeeper Katarzyna Kiedrzynek.
Frankfurt found a way through however after 32 minutes when Sasic picked up a centre from Kerstin Garefrekes to head past Kiedrzynek.
The Parisians reacted with Marie-Laure Delie equalising after 40 minutes, but watched by German chancellor Angela Merkel, Islacker, 26, grabbed the winner two minutes into extra time as PSG's Shirley Cruz Trana missed a last-gasp effort before the final whistle.
It was the end of the adventure for Paris Saint-Germain who had been competing in their first final, and whose fortunes have been transformed since the club was taken over by Qatar Sports Investments in 2011, with the women's team turning professional the following year.
"I can't find the words to express my disappointment," said defender Laure Boulleau.
"We had a fabulous run, eliminating Lyon and Wolfsburg, and really wanted to give something back to PSG.
"We have to turn the page now and focus on 'Les Bleus'. There are lots of things to do with this fabulous team," she said, with three weeks to go before the World Cup in Canada.
PSG's Qatari chairman Nasser Al-Khelaļfi, in Berlin for the match, said: "We have all the qualities to win the Champions League, we'll try against next year.
"They had a great match, it's great experience for us."
Having finished third in the women's Bundesliga behind winners Bayern Munich and Wolfsburg, Frankfurt had missed out on qualifying for next season's Champions League, and needed a victory.
German clubs have now won nine of the 14 editions of the elite European tournament, with the victory boosting German hopes of a third World Cup title in Canada.