A powerful first quarter from Unicaja saw the Malaga-based team trump UCAM Murcia 96-86 with Ryan Toolson (21 points) and Fran Vazquez (15 points, 10 rebounds) leading the way for the victors.
The victory took Unicaja into second in the Spanish basketball league, just behind Real on points difference, while Barcelona slipped to third after losing 85-74 at Sevilla.
Real, meanwhile, failed to stay clear top of the table as Unicaja matched their record after the powerhouse lost 89-84 to Estudiantes.
In Madrid on Sunday, Estudiantes welcomed their more-fancied city rivals with a record of just 2-7 and looked in trouble at half-time as Real led 45-34 but a 27-18 final quarter saw the hosts triumph in the shock result of the round.
Nacho Martin (19) top-scored for Estudiantes, while Real's Felipe Reyes (21) battled gamely for the visitors.
The win took Estudiantes to 13th in the standings.
In Seville, the home side dominated from the outset, keeping reigning champions Barcelona to less than 20 points in each of the first three quarters to eventually win by nine.
Willy Hernangomez sank 29 points and hauled down 13 rebounds for Sevilla, as they notched just their third win of the campaign.
Real and Unicaja (9-1) sit above Barcelona (8-2), while Bilbao sit fourth after an 80-67 loss to Gipuzkoa.
Bilbao's loss allowed FIATC Joventut to join them on a 7-3 record, the latter having accounted for Gran Canaria 81-79.
In other results, Tenerife defeated La Bruixa d'Or 66-62, Valencia overcame Laboral Kutxa 85-70, Fuenlabrada crushed BC Andorra 88-65 and Zaragoza prevailed 82-74 against Rio Natura Monbus.