Rybakina and Pegula battle into Adelaide quarters, Shelton advances in Auckland
Top-seeded Rybakina prevailed 6-3, 7-5 against Spaniard Bucsa though the scoreline does not quite reveal how intensely they fought producing 90 minutes of high-quality tennis.
Rybakina broke Bucsa in the eighth game, which was just enough for the Kazakh to secure a tight opening set in the Australian Open warm-up event.
Bucsa fought tooth and nail but her failure to convert any of the four break points that came her way cost her the set.
Rybakina began the second set by breaking her opponent but it was not to be a cakewalk for the top seed.
Bucsa finally converted a break point en route to a 4-3 lead but Rybakina somehow managed to dominate the big points and sealed her victory with an ace.
"I think she played really well today," Rybakina said of her opponent.
"I didn't start that quick with the movement and everything but I think she played really well, especially coming forward, which you don't see much in women's tennis.
"It was a bit surprising for me, but yeah, happy that I managed to win."
World number five Pegula battled back from a set down to overcome lucky loser Bernarda Pera 4-6, 6-2, 6-3 in an all-American clash.
Pegula looked ill at ease against Pera's powerful left-handed game in the opening set and converted only one of her 10 break-point chances.
But she found her feet in the second set to draw level and after nosing ahead by a break at 4-3 in the third she then saved five break points for a crucial hold.
Her sixth break in the next game vanquished Pera, setting up a quarter-final against Anastasia Pavlyuchenkova on Thursday.
Former French Open champion Ostapenko had an injury scare before overpowering Caroline Garcia 6-4, 5-7, 6-4 to reach the quarter-finals.
Leading 5-4 in the opening set of what turned out to be a hitting contest, Ostapenko took a medical timeout after complaining of sharp pain in her left thigh.
She returned to secure the set but Garcia forced the decider with her spirited comeback in the second.
Ostapenko, playing with a strapped thigh, broke her opponent in the opening game of the third set and made her fourth match point count to prevail in two hours and 41 minutes.
At the Hobart International, another tune-up event for the Melbourne Park Grand Slam, top seed Elise Mertens defeated Anna Karolina Schmiedlova 6-2, 6-3 to make the quarter-finals.
Qualifier Yuan Yue, who stunned former US Open champion Sloane Stephens on Tuesday, maintained her strong run with a 7-5, 6-3 upset win against fourth seed Wang Xinyu.
At the Auckland Classic, top seed Ben Shelton defeated Fabian Marozsan 6-3, 6-4, while third seed Francisco Cerundolo was hammered 6-1 6-1 by Alexandre Muller.
Arthur Fils, who ended Richard Gasquet's title defence on Tuesday, swept aside Nuno Borges 6-2, 6-0 in 52 minutes to storm into the last eight.