Federer lost only seven games in wins over Cameron Norrie and Frances Tiafoe but found it tougher in his first match against Tsitsipas.
David Ferrer, who had earlier defeated Lucas Pouille in his final singles match in Australia, was duly partnered by American Whitney Osuigwe in the doubles contest, which Cornet and Pouille won 4-2 4-2.
Australia got a consolatory victory in the doubles match, winning against the German duo 4-0, 4-3.
It was the prefect preparation for the Australian Open as Roger Federer teamed up with Belinda Bencic to help Switzerland defend its Hopman Cup title in Perth.
She will meet Karolína Plíšková of the Czech Republic, who triumphed against Ajla Tomljanović of Australia 6-1, 1-6, 6-1.
The world No 2 secured an early lead for the Germans by beating Ashleigh Barty 6-4 6-4 in the best-of-three tie.
The semi-finals will take place tomorrow.
Zverev and Kerber were despondent after the loss and the former said it was a tough pill to swallow.
The crowd was appreciative of Switzerland's achievement but Zverev roasted Federer when given his chance with the microphone at the trophy presentation after the tie.
Alexander "Sascha" Zverev and his compatriot Angelique Kerber lost by just one point in the mixed doubles final at the Hopman Cup in Perth, Australia, but he didn't let Roger Federer enjoy his trophy prize easily, deciding to roast him in hilarious fashion.
A record 110,364 people attended what is rumoured to be the final Hopman Cup over the past week. We were one shot away.
Smashing their way through the first set 4-0, Federer and Bencic looked like they would breeze past the Germans. "The guy had a super, super strong last five or six months of the year".
Zverev had evened up the head-to-head stats with Fed last year with some decisive victories, especially finishing up the year at the ATP Finals event as the victor. Kerber takes the match, winning the hard-fought two sets 6-4 7-6 (6).
Under the short sets format, the match is decided by a winner-takes-all point if scores are locked at 4-4 in the third-set tiebreak.
Kerber had two match points at 6-4 in the tie-break, but Bencic again hung on grimly and won the next two points.
Zverev talked of hoping to return next year, and Bencic admitted, "I would love every week to play Hopman Cup!".