It kept Zidane's men on track to win the league title, although they remain second to Barcelona but are level on points and hold a game in hand.
Cristiano Ronaldo scored his 400th competitive goal for Real Madrid as the title hopefuls took control of their LaLiga clash with Sevilla at the Bernabeu.
Defender Nacho Fernandez put Real ahead in the 10th minute with some quick thinking from a free kick, sidefooting the ball into the bottom corner and flummoxing Sevilla who were still preparing their defensive wall.
Real Madrid coach Zinedine Zidane lauded Cristiano Ronaldo, saying his superstar forward always seemed to deliver in big moments.
Barcelona beat Las Palmas 4-1 with Neymar scoring a hat-trick.
Sevilla's defeat at the Bernabeu also guarantees they will finish fourth and Atletico Madrid, who drew 1-1 at Real Betis, qualify automatically for next season's Champions League in third.
Sporting Gijon were relegated despite winning 1-0 at Eibar as tiny Leganes secured a 1-1 draw at Athletic Bilbao which ensured they remain in La Liga for another year after being promoted to the top flight for the first time last season.
That goal meant Madrid broke Bayern Munich's European record for scoring in consecutive games as their streak now stretches to 61 games.
Jovetic then saw a fine chipped effort come back off the bar and was denied by Keylor Navas when played through by Joaquin Correa as Sevilla continued to threaten.
Ronaldo has played just 391 games for Real and is the club's most prolific goalscorer in their long history.
The visitors more than matched Real until Ronaldo struck his second of the match in the 78th minute, a great team move resulting in Toni Kroos breaking in to the box, the German pulling the ball back to just inside the penalty area for Ronaldo to smash the ball in off the underside of the crossbar with an excellent strike.
Kroos helped set up that strike and it was the Germany worldwide who rounded things off when he slid in Real's fourth six minutes from time.
Neymar and Luis Suarez struck before the half-hour mark, but Pedro Bigas halved the deficit after 63 minutes.
But Neymar headed home Ivan Rakitic's cross and then sealed his first hat-trick of the season 19 minutes from time.