Federer, the No. 1-seed, beat eighth-seeded Jeremy Chardy 6-3, 6-7 (3-7), 6-3 after the unseeded Hewitt gained his spot in the championship match with a 5-7, 6-4, 6-3 upset of No. 2-seeded Kei Nishikori.
The matches were played in sweltering conditions with temperatures topping 104 degrees Fahrenheit.
Nishikori took the early advantage against Hewitt with a break in the 11th game but Hewitt broke through on his ninth break-point opportunity for a break in the 10th game of the second set. He broke Nishikori's serve again to open the third set and held on for the win in 2 1/2 hours.
Federer had 20 aces and faced just one break point, which he saved, in beating Chardy in just less than 2 hours. Federer won 72 percent of the points on serve. A break in the eighth game of the third set proved to be the difference in the match.
Federer enters Sunday's final with an 18-8 edge in career meetings versus Hewitt, a rivalry that had its first chapter in 1999. Federer is 77-36 in ATP finals and a win Sunday would leave him alone in third place on the all-time list for ATP titles.
Hewitt, playing in his first final in his homeland since the 2005 Australian Open, is 28-16 in championship matches. However, he hasn't won since June 2010, when he beat Federer for the title at Halle, Germany.