Chasing a modest 181 for victory from their allocation of 50 overs, Zimbabwe reached the target with 21 balls to spare on Monday.
Piet Rinke hit the top score of 42, but it took an unbroken stand of 40 between Gregory Strydom, who scored 23 not out, and Keith Dabengwa, not out on 15, to get the visitors home.
The Zimbabweans had declined to 141 for six in the 31st over, before Strydom and Dabengwa settled their nerves.
Earlier, Daniel Thomas hit the top score of 33 for Antigua and Barbuda and Gavin Williams supported with 31 in a sixth-wicket stand of 44 that brought some respectability to the home team's total of 180 from 43.2 overs.
The two sides meet in another limited-overs practice match on Tuesday at the same venue.
Antigua and Barbuda 180 off 43.2 overs (Daniel Thomas 33, Gavin Williams 31, Gavin Tonge 26, Austin Richards Jr 22; Ngonidzashe Mahwire 2-20, Prosper Utseya 2-20, Keegan Meth 2-24).
Zimbabwe 181 for six off 46.3 overs (Piet Rinke 42, Gregory Strydom 23 not out, Brendon Taylor 23, Elton Chigumbura 22, Chamunorwa Chibhabha 22; Gavin Tonge 2-41).