Frankfurt, already champion in 2002, 2006 and 2008 and a finalist in 2004 and 2012, is 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 its rivals with 40 goals for just two conceded in eight matches, it had to battle past the French novice.
The Ligue 1 runner-up, which had eliminated French champion Lyon and two-time defending champion Wolfsburg en route to the final, held firm for the first 30 minutes largely thanks to the efforts of 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.
PSG reacted immediately with Marie-Laure Delie equalising after 40 minutes after a centre from Kenza Dali to head past Desiree Schumann in the Frankfurt goal.
Frankfurt pushed for the winner in the second half without success with Kiedrzynek holding firm faced with a barrage of shots from Sasic, Veronica Boquete and Peggy Kuznik.
But watched by Germany 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.
Having finished third in the women's Bundesliga behind winner Bayern Munich and Wolfsburg, Frankfurt had missed out on qualifying for next season's Champions League, and needed a victory.
It was a cruel end to the adventure of the PSG women's team which was amateur until three years ago and was playing its first European final.
German clubs have now won nine of the 14 editions of the elite European tournament.
The victory also boosted Germany hopes three weeks before the FIFA Women's World Cup in Canada.
