IT was a critical prelude to a piece of Hopman Cup history, but Serena Williams believes she has already taken an important first step towards possible Australian Open glory.

Pitted against Greek Maria Sakkari, Williams overcame nerves and a swath of unforced errors to win 7-6 (7-3) 6-2 - her first victory Down Under since lifting the 2017 Australian Open crown.

Levelling the tie with Greece, the American already has her sights set on two more pressing goals.

She will on Tuesday night come face to face for the first time in competitive battle with fellow grand slam legend Roger Federer in mixed doubles.

The pair, both 37 and in career twilight, owns a combined 43 singles majors. Williams has 23, Federer 20.

Desperate to match Margaret's grand slam record of 24 singles crowns, Williams is on a mission - as evidenced by occasional bursts of emotion against world No 41 Sakkari.

"It's great to be out in match day and it's great to be back here," she said.

"As you know, I love playing down here, Down Under and here in Perth in Australia.

"Some of my best memories are here."

Ranked No 16 in the world after a comeback from starting a family, Williams is excited about jousting with Federer.