The former world number one looked to be on course for a straightforward victory after taking the first two sets 7-5 6-3.
However a medical timeout for Wawrinka saw him return in much better form, and took the next two sets 6-1 6-4.
Federer then took a timeout of his own, and he was able to prevail in the deciding set by 6 games to 3.
It means Federer is now the oldest men's Grand Slam finalist in over 45 years, and is one win away from a record 18th Grand Slam title.
He'll play either Rafa Nadal or Grigor Dimitrov in Sunday's final.
Earlier the Williams sisters both secured their place in Saturday's women's final.
Serena strolled past Mirjana Lucic-Baroni 6-2 6-1, while Venus needed three sets to see off Coco Vandeweghe.
Saturday's match will be the ninth Grand Slam final between the pair and the first in nearly eight years.
