Clijsters's former fiance Lleyton Hewitt, however, struggled to clear the hurdles presented by Canadian Frank Dancevic before lunging into the third round with a 6-4, 6-4, 3-6, 6-4 victory.
Hingis and Clijsters entered the two showcourts at Melbourne Park at almost the same time for their second-round matches, both eager to get back to the locker room the quickest.
Fourth seed Clijsters crossed the tape first, whipping Japan's Akiko Morigami 6-3, 6-0 in 59 minutes under a closed roof in the Rod Laver Arena.
Hingis, seeded sixth, lagged behind by nine minutes but was impressive in a 6-2, 6-2 win over hapless Russian teenager Alla Kudryavtseva.
Clijsters, aiming to add the Australian Open title to her 2005 Flushing Meadows success, said: "We almost won at around the same time and then we came into the locker room and she's like, 'Damn, you beat me, you were there first'."
After struggling to stay on her feet during a three-hour battle in the roasting conditions two days ago, Maria Sharapova's ruthless streak was back on show on Thursday.
She whizzed around court as if she was on roller skates and flattened Russian compatriot Anastassia Rodionova 6-0, 6-3 in 58 minutes.
Blowing kisses around court, the top seed said: "My brain cells were working today unlike my previous match.
"I'll be fine. It was good to get a quick one in today."
Sharapova led the Russian charge at the championships as one of eight women from her nation through to the third round.
BEARDED BLAKE
Fans can look forward to seeing a lot more of a bearded James Blake after he dispatched fellow American Alex Kuznetsov 6-4, 6-1, 6-2.
"Once I start winning, I don't shave, it's a superstition," the fifth seed, who won the Sydney International title last weekend, told the crowd.
"Once something starts working you've got to stick with it."
British teenager Andy Murray could have done with sticking to the form of his previous match.
The 15th seed, who dropped only one game in the first round, was made to hang around a lot longer for a 7-6, 7-5, 6-4 win over Spanish left-hander Fernando Verdasco.
Burly Argentine David Nalbandian set up an intriguing third-round showdown against Frenchman Sebastien Grosjean following a 6-4, 6-4, 6-4 triumph over Nicolas Lapentti.
Hewitt gave his army of hollering fans plenty of anxious moments as he continued his mission to end Australia's search for their first men's champion since 1976.
Having come into the tournament with a question mark hanging over his fitness, he was happy to follow up his previous five-set win with a two-hour, 48-minute battle on Thursday.
Firing pin-point serves, the 19th sent down 14 aces. But the fiery Australian almost wiped out all the free points by producing 12 double faults.
"Coming in, I didn't have too much match practice and I've now had a lot of match practice. That can only be a good thing," said Hewitt, who is seeded to meet world number two Rafael Nadal in the quarter-finals.
