Andreescu, who was also beaten by the 58th-ranked Frenchwoman less than two weeks ago on grass in Berlin, struggled to hit anything on target and even luck deserted her on Court Two.
Canadian Andreescu, 20, served for the match at 5-4 in the deciding set but Zidansek broke back before missing a match point of her own in a gripping finale.
Andreescu found herself in trouble again serving at 7-8 and this time was unable to dig her way out of trouble with world number 85 Zidansek winning in three hours and 20 minutes.
Kvitova, the former Wimbledon champion and Melbourne runner-up in 2019, committed 44 unforced errors in her 6-4, 1-6, 6-1 defeat to Romania's Sorana Cirstea.
