Defending Open champion Madison Keys prevailed 6-4 6-3 over fellow American McCartney Kessler, while world No.1 Aryna Sabalenka destroyed Spain's Cristina Bucsa 6-0 6-1 in 48 minutes.
Both have to get through third-round clashes but world No.7 Keys, who beat Sabalenka in three sets in last year's Australian Open final, is aware of the dangled carrot and the challenge ahead of her.
"The reality of this week is that it is a very tough draw. Hopefully that (playing Sabalenka) happens because it means I've won another match," Keys said.
"I think that it is always great to have to play the best players and see where you are at. If you win that match it is a great win and there are always a lot of things you can learn, no matter what happens.
"I knew it was going to be a tough match. It's always a little nerve wracking playing your first match of the year so it felt like I was trying to knock a bit of the rust off, but overall very happy."
Keys was undefeated in Australia last year to claim the Adelaide International and Australian Open.
"Last year was a dream come true," Keys said.
"I would obviously love a repeat of last year but that is asking for a lot if you are trying to leave the country undefeated. That is always the goal and so far so good."
Sabalenka was a force of nature against Bucsa, who was never in the contest.
The Belarusian was a powerhouse from the back of court and devastating at the net to breeze through the first set in 22 minutes.
In just 48 minutes the match was over, with Sabalenka stunning the crowd at Pat Rafter Arena with the sheer brutality of her shots.
World No.28 Bucsa is no slouch but Sabalenka was on another level.
"Let's just first get to the quarter-finals and then we can talk about the (Keys) match but if it happens it is going to be a battle. We always bring a great battle on court and always a great level," Sabalenka said.
"I would love that to happen."
Men's action was far less predictable, with fourth-seed Tommy Paul knocked out by big-serving French danger Giovanni Mpetshi Perricard 7-6 (7-2) 3-6 7-6 (8-6).
Paul joined second-seed Alejandro Davidovich Fokina on the scrap-heap, the Spaniard upset by American Brandon Nakashima 7-6 (7-4) 6-4.
And fifth-seeded Canadian Denis Shapovalov lost to Belgian world No.84 Raphael Collignon 6-4 6-2.
Former tournament winner Nick Kyrgios, in his first ATP Tour match since March, lost in 66 minutes to American world No.58 Aleksandar Kovacevic 6-3 6-4 later on Tuesday.
In men's doubles, Cruz Hewitt, son of legend Lleyton Hewitt, lost his round-of-32 match with fellow Australian James Duckworth 6-4 7-5 to Brazilian duo Rafael Matos and Orlando Luz.
