Real need to win to keep the pressure on Barcelona who can not afford to lose their game against Las Palmas.
Sevilla were on the back foot for most of the half but they almost pulled a goal back in the 32nd minute when Jovetic's lob crashed against the crossbar.
The fight for the La Liga title will go down to the last day of the season after convincing wins for Real Madrid and Barcelona on Sunday left them locked together on 87 points at the top of the table.
Real were out of the blocks quickly and took the lead after just 10 minutes in hugely controversial fashion.
The club faced Sevilla, and while Cristiano Ronaldo managed to get his 400th and 401st goal for the club, Keylor made key saves in the game at vital points, and his manager made sure to point that out after the game, amid growing speculation the club are set to sign David De Gea in the summer.
Sevilla were still putting their wall together when Nacho lifted the ball into an unguarded net.
France global Lucas Digne was chosen in the unfamiliar role of right back due to the shortages in defence and risked getting sent off early with a last-ditch tackle on Jese but was only shown a yellow card.
Neymar and Luis Suarez struck before the half-hour mark, but Pedro Bigas halved the deficit after 63 minutes.
Madrid remain in the driving seat after the European champions saw off Sevilla 4-1 as they have two games remaining to Barca's one. But Alexander Szymanowski equalised on the hour with a header that meant so much for Leganes.
The Canarian outfit have enjoyed a very solid season in La Liga, and have guaranteed themselves another season in the top flight with games to spare.
Villarreal, Athletic and Real Sociedad are the teams still fighting for the two Europa League spots. That match in hand will be played on Wednesday against a Celta Vigo side who suffered another body blow earlier yesterday when they were beaten 3-1 by Copa del Rey finalists Alaves.
And that became five successive losses as in-form Alaves scored three times in the opening 37 minutes, Manu Garcia making the most of a defensive mistake to put the hosts ahead early on before Zouhair Feddal and Deyverson also got on the scoresheet.