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Australia captain Hewitt was his country's leading player when it last reached a Davis Cup final 19 years ago and he was just as thrilled as his charges caused caused a boilover to set up a showdown for the trophy against Canada or Italy.
Max Purcell and Jordan Thompson beat the Olympic champion pair of Nikola Mektic and Mate Pavic in the deciding doubles to earn a 2-1 team victory.
Borna Coric got the better of Thanasi Kokkinakis in the first rubber, earning a 6-4 6-3 victory to put Croatia in the driving seat.
After a shock title success at the Cincinnati Masters in August, Coric was looking to end his year on another huge career high.
However, Marin Cilic could not seal the deal for Croatia as he slumped 6-2 6-2 to Alex de Minaur in a surprisingly one-sided match that followed.
De Minaur broke the Cilic serve four times and held his own throughout, typically with plenty of comfort, as he took down the 2014 US Open champion.
That meant the contest came down to the doubles, and Purcell and Thompson held their nerve in a gargantuan battle with Mektic and Pavic, coming from behind to score a 6-7 (3-7) 7-5 6-4 victory.
1️⃣9️⃣ YEARS LATER!
— Davis Cup (@DavisCup) November 25, 2022
Australia defeat Croatia 2-1 to book their place in the Final for the first time since 2003 👏#DavisCup #byRakuten | @TennisAustralia pic.twitter.com/bBhMiHOv9A
"I couldn't be prouder of the whole team," Hewitt said, quoted on Tennis Australia's website.
"We knew we were the underdogs coming into this today and we like being in that position. It's a place I really enjoyed as a player and also as a captain."
Hewitt was a star of the team when Australia last won the Davis Cup or even made the final, in 2003. That was the country's 28th triumph in the competition, and now it has a chance to go after number 29.
"To put us in the final, that feeling, I can't describe it," Thompson said.