Germany were leading Australia 2-0 following Saturday's play in the semi-final encounter, meaning Kerber knew another triumph on the hard court of the Pat Rafter Arena in Brisbane would confirm victory, and she duly delivered a 4-6 6-0 6-4 triumph.
Stosur had won both of the previous encounters between the pair and looked well-placed to repeat that feat after taking the opener.
However, Kerber soon rallied and reeled off seven straight games to grab the initiative.
Although she missed the chance to serve out victory when 5-2 up in the decider, she made no mistake the second time around, finishing off in style with an ace.
Speaking after the win, Kerber said: "It's a very special moment for me and the whole team.
"It feels very great. I played a good match but it was a tough one because Sam was playing also very tough and I have never beaten her before. It just means a lot."
With Germany's progression sealed, the fourth singles rubber between Casey Dellacqua and Andrea Petkovic was cancelled, but the former did partake in the doubles with Ashleigh Barty and the pair restored some pride for Australia by defeating Julia Goerges and Anna-Lena Groenefeld.
Awaiting Germany in the final are neighbours Czech Republic, who whitewashed Italy 4-0 in Ostrava.
Petra Kvitova cruised past Roberta Vinci 6-3 7-5 in the third rubber to give the Czechs an unassailable 3-0 lead, meaning the last singles encounter between Lucie Safarova and Camila Giorgi was cancelled.
Safarova was part of a winning doubles pair with Klara Koukalova later on Sunday as the champions in 2011 and 2012 reached a third final in four years.
Czech Republic will host the final, which takes place on November 8 and 9.