The Frenchman's Real side also broke the Madrid club's record for consecutive league wins, overtaking the 15-game winning streak
Real Madrid brushed off the absence of Cristiano Ronaldo and Gareth Bale to beat Espanyol 2-0 away and maintain their 100 percent start to the league season while matching the La Liga record of 16 consecutive victories.
James Rodriguez scored his first Real goal in five months to give the visitors the lead in stoppage time before the break and Karim Benzema sealed the points in the 70th minute with a close-range finish past former Madrid goalkeeper Diego Lopez.
Athletic Bilbao beat Valencia 2-1 to pile more pressure on the visitors' beleaguered coach Pako Ayesteran, Villarreal downed Real Sociedad 2-1 thanks to a sensational 50-yard strike from Nicola Sansone, while Celta Vigo drew 0-0 at Osasuna.
Real stay top of La Liga on 12 points, three above Barcelona and Las Palmas, having equalled Barca's record of 16 straight league wins achieved under Pep Guardiola in the 2010/11 season.
"We played a great game from the start with concentration and enthusiasm. The best way to get the points is to come out fired up like we did today," Zidane told Movistar Plus.
The Frenchman's Real side also broke the Madrid club's record for consecutive league wins, overtaking the 15-game winning streak under Miguel Munoz in the 1960/61 season.
"Of course, the record means a lot to us because it's proof of the phenomenal work all the players are doing. Getting points is the most important thing but it's also nice to have a record like this," added Zidane.
Ronaldo missed the trip to Espanyol with a sore throat, having scored five goals in a 6-0 thrashing last season, while Bale is recovering from a hip injury sustained in Wednesday's last-gasp 2-1 Champions League win over Sporting Lisbon.
The absence of the pair allowed Lucas Vazquez and Marco Asensio to face their former club, while Rodriguez came in for Germany international Toni Kroos in midfield.
Colombia's 2014 World Cup Golden Boot winner has not enjoyed a consistent run in the side since Zidane took charge but seized the opportunity, nutmegging an Espanyol defender outside the area and stroking the ball into the bottom corner of the net.
Benzema had looked far from match fit against Sporting but was given another chance by Zidane and, after having an effort ruled out for offside in the first half, the Frenchman tapped in Asensio's low cross to finish off a classy team move.
Villarreal forward Sansone scored from just over the halfway line as they beat Sociedad to move up to sixth in the table, level on eight points with Atletico Madrid and Sevilla.
The 13 million euros ($14.50 million) close-season signing from Serie A side Sassuolo let fly from the right hand side of the field to beat goalkeeper Geronimo Rulli in the 25th.
Italian Sansone had also given the hosts the lead three minutes earlier from inside the box after the Brazilian former Chelsea striker Alexandre Pato had missed a penalty.
Sociedad's Yuri reduced the deficit in the 35th minute but they finished the game with 10 men after fellow defender Joseba Zaldua was sent off in the 89th for a second yellow card.
Athletic Bilbao came from behind to beat Valencia, who are bottom without a point or a goal from their four games.
"Now is the time to reflect on what we're doing and make a real effort to turn things around on the pitch," said Valencia goalkeeper Diego Alves. "We have a good enough team to improve on where we are at the moment."
Alvaro Medran gave Valencia a dream start by scoring in the second minute but their former striker Aritz Aduriz turned the game in Athletic's favour with two strikes before halftime.
Second-bottom Celta Vigo got their first point of the season in a goalless draw at promoted Osasuna, who are a point and a place above them in the standings.
(1 = 0.8965 euros)