The champions returned to third place in the standings on Wednesday for the first time since the start of December after beating Leganes 3-1 in their game in hand, climbing above Valencia and moving 14 points behind leaders Barcelona.
Real have also thrashed Real Sociedad 5-1 and Real Betis 5-3 within the last two weeks as well as beating Paris St Germain 3-1 in the first leg of their blockbuster Champions League last-16 tie, with their recent form contrasting with their limp start to the campaign.
They are seven points from Atletico Madrid in second and with Diego Simeone's side facing a difficult trip to Sevilla on Sunday, Real have the opportunity to put further pressure on their local rivals.
"I'm proud of everything we're doing at the moment, we are showing character and personality, and scoring 26 goals in the last six games is lovely," Zidane told a news conference on Friday. "We want to continue on this great run and tomorrow we want to put in a good performance."
Alaves have also turned a corner after an abysmal start to the season saw them lose nine of their first 10 games, with new coach Abelardo Fernandez leading the Basque side to four wins from their last six to move 10 points clear of the relegation zone.
"We know they've changed coach and have a squad that never gives up, but right now we're in very good shape," added Zidane.
Real have a kinder schedule than Atletico between now and the international break which begins on Mar. 19, with Simeone's side visiting Barca a week after their game with Sevilla, while Zidane's side face Espanyol away after the Alaves game followed by a home game against Getafe.
Zidane also apologised to midfielder Dani Ceballos for bringing the player on for the final 30 seconds against Leganes.
Ceballos, a 10-million-euro signing from Real Betis last summer, has made only two Liga starts since joining Madrid.
"I felt very bad about it and I'm very sorry and I've told him so. I don't like to bring a player on for 30 seconds for nothing," Zidane said.
"He knows he hasn't had many minutes but he has kept on working hard, he's stupendous. I like him a lot and he has to keep on working."
(Reporting by Richard Martin; Editing by Peter Graff)
