Colette Cavanagh's 17th-minute thunderbolt and a second-half Jamie-Lee Napier brace was enough to secure all three points in the searing heat against Georgian outfit FC Nike.
In truth, the Capital side were head and shoulders above their opponents and should have won more handsomely.
Hibs have been in drawn in Group 3 alongside hosts Pomurje Beltinci and Cardiff Met with the winner progressing to the last 32 of the competition.
The SWPL and Scottish Cup holders now face Cardiff on Saturday before they round things off against Beltinci next Tuesday.
Head coach Grant Scott made five changes to the starting XI that lost 2-1 to Glasgow City on Sunday – Siobhan Hunter, Amy Muir, Cailin Michie Lauren Davidson and Kirsten Reilly all dropping to the bench. Cavanagh, Clare Williamson, Ellis Notley, Siobhan Higgins and Amy Gallacher their replacements.
And Cavanagh's inclusion was vindicated just after the quarter of an hour mark when she rifled home an effort into the top right-hand corner from just outside the box.
Napier made things more comfortable midway through the second half with an astute finish before adding her second right at the death.