Frenchman Zidane was brought back to the Spanish giant after previous coach Santiago Solari was sacked following a string of poor results.
The 46-year-old Zidane, who oversaw three consecutive Champions League titles with Real, picked out-of-favor Isco for his first start since October and was rewarded when the Spaniard scored in the 62nd minute.
Welshman Bale, who has also been under pressure at Real in recent months, added a second after 77 minutes to restore some pride at the Santagio Bernabeu.
Real is third in the La Liga table, two points behind Atletico Madrid and nine behind leader Barcelona.
Zidane resigned after last year’s Champions League final victory against Liverpool, but was asked to return this week by club president Florentino Perez.
The former Real striker replaced his ex-teammate Solari, who was promoted to the role of coach after Julen Lopetegui was dismissed following a poor run of form in October.
Zidane has taken over with Real having little to play for except ensuring it qualifies for next season’s Champions League.