Japanese second seed Naomi Osaka extended her winning streak to a 23rd match as she moved into the Miami Open quarter-finals for the first time.
Osaka, whose unbeaten run includes claiming the US Open and Australian Open titles, won 6-3 6-3 against Belgium’s 16th seed Elise Mertens.
Barty won 6-1 1-6 6-2 in a gripping contest with the 2020 US Open finalist.
Barty, playing in an overseas tournament for the first time in more than a year because of the coronavirus pandemic, continues her title defence against Belarusian seventh seed Aryna Sabalenka.
Osaka will face Greek 23rd seed Maria Sakkari or American 29th seed Jessica Pegula next.