Barcelona loanee Munir crossed the ball in for Garcia and the Alaves skipper made no mistake directing a close-range header past Navas off the underside of the bar.
Zinedine Zidane's side nearly made the game safe when Cristiano Ronaldo's drive cannoned back off the post, though up the other end, Alaves were also denied by the woodwork, Alfonso hitting the frame of the goal from distance.
Real Madrid have announced that Marcos Llorente has signed a new four-year contract.
Just three minutes later, however, Pacheco's punch to clear a corner dropped in front of Ceballos on the edge of the box, and the midfielder connected with his volley sweetly to restore Madrid's advantage just before the break.
Ronaldo's afternoon ended with Pacheco tipping his angled strike around the post, but Madrid nonetheless held on for the three points. Marco Asensio played in Ceballos, who cleverly cut the ball back before finishing the chance for the lead.
Real Madrid boss Zinedine Zidane has no concerns over Cristiano Ronaldo's form despite the forward failing to score for a second straight match on Saturday. Spanish born Ghanaian striker Inaki Williams scored two goals for the latter.
Pacheco made two super saves to deny Vazquez and Ronaldo in the final 10 minutes, but 2-1 was how it finished as Real Madrid returned to winning ways against an Alaves side that have now lost all six of their league matches this season. Alaves, meanwhile, are next in La Liga action away to Levante next weekend.