After a goalless first half, in which both sides had hit the woodwork, Yannick Carrasco opened the scoring in the 46th minute.
If Barcelona beat Girona on Saturday evening, they will reclaim a seven-point lead over their bitter rivals at the top of the table.
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.
Real Madrid's number seven looked certain to be sending the away side 3-1 ahead in the 63rd minute after curling a lovely effort towards the far corner, but the post saved Alaves as the 32-year-old was denied once again.
Ceballos caught Madrid's eye in the offseason after he was named the best player at the Under-21 European Championship, where he helped Spain reach the final before losing to Germany 1-0.
The first of Ceballos' goals came in the 10th minute after a brilliant cut back on the edge of the box from Marco Asensio.
Cristiano Ronaldo returned for Real Madrid, who were looking for a home win after two consecutive draws in the Liga Santander in front of their fans on Wednesday, reports Xinhua news agency.
Pedraza hit the Real Madrid woodwork for the second time in the 76th minute following a mistake from Varane, and a late goal or two appeared certain with both defences looking shaky in the second period.