Gauff, Rybakina cruise into Dubai last 16
The American, who lost to lucky loser Elisabetta Cocciaretto in her opening match in Qatar, made no such mistake against Kalinskaya, easing through the second-round tie 6-4, 6-4.
Gauff will face Belgian Elise Mertens in the last 16 of the WTA 1000 event.
The two-time Grand Slam champion created headlines earlier this week for comments about anti-immigration policies in the United States, saying: "I don't think people should be dying in the streets for just existing."
Gauff struggled at times in Dubai, serving 12 double-faults, but broke Russian Kalinskaya's serve six times to emerge victorious from a scrappy encounter.
"It wasn't the prettiest one, but it was enough for today," said Gauff, seeded third.
"It was pretty windy. I was just trying to adjust -- both of us were struggling with consistency on the court."
Australian Open champion and top seed Rybakina put on an imposing display as she brushed past Kimberly Birrell 6-1, 6-2 in just 60 minutes on court.
"Overall, I'm happy with the result, with the match, and now I just need to rest and prepare for tomorrow," Rybakina said after getting back to winning ways following a quarter-final exit in last week's Qatar Open.
The Kazakh will take on Croatian lucky loser Antonia Ruzic in the last 16, following her 6-1, 6-7 (2/7), 6-1 victory over Anastasia Zakharova.
Mirra Andreeva and Belinda Bencic were both beneficiaries of second-round walkovers.
Russian teenager Andreeva, who received a first-round bye, will face Romanian Jaqueline Cristian for a quarter-final place after Daria Kasatkina pulled out of their match with a hip injury.
In-form Czech youngster Sara Bejlek, who won a title in Abu Dhabi earlier this month, also withdrew with an abdominal injury, handing Bencic a spot in round three.
The Swiss player will next face seventh seed Elina Svitolina, who progressed to the round of 16 after her opponent, Paula Badosa, retired after losing the opening set.
American fourth seed Jessica Pegula cruised through with a 6-4, 6-0 thrashing of Varvara Gracheva and will next play compatriot Iva Jovic.
Alexandra Eala beat sixth seed Jasmine Paolini 6-1, 7-6 (7/5) to set up a meeting in the next round with Sorana Cirstea.
The tournament in Dubai, one of the 10 WTA 1000 events, has been severely hit by the withdrawals of world number one Aryna Sabalenka and six-time Grand Slam champion Iga Swiatek.
Second seed Amanda Anisimova had also been given a walkover on Monday after her second-round opponent Barbora Krejcikova pulled out.
Canadian teenager Victoria Mboko, who reached the Qatar Open final last week, also withdrew ahead of the tournament, citing an elbow injury.