Joel Freeland was the hero for the Spanish side in Malaga, the Briton leading his side with 21 points - seven of which came in OT - and 12 rebounds.
Kristaps Valters weighed in with 20, including two clutch three-pointers in the extra period, to see Unicaja over the line and hand them their first win of the new season.
Tremmell Darden added 10 points while Berni Rodriguez was deadly in the closing minutes of regulation time with two free-throws that levelled the scores at 67-67.
For the visitors, Sonny Weems was largely responsible for their sterling regulation time performance with 21 points and eight rebounds.
Marko Popovic netted 18 and Mantas Kalnietis had 11 but their cause was not helped by a high number of turnovers - 20 for Zalgiris to Unicaja's nine.