Ward beat Frenchman Jonathan Eysseric in straight sets 6-3 6-1; while Baltacha weathered a fightback from American Melanie Oudin to take her match 6-1 3-6 6-2.
They are both now two victories away from a place in the main draw of the final Grand Slam of the year in New York.
British number two Ward next meets Matthias Bachinger of Germany while Ukrainian Olga Savchuk awaits Baltacha.
Dan Evans, Tara Moore and Samantha Murray are also bidding to make it through to the tournament proper.
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