Sevilla's first of those will be against Real Madrid on Sunday at Valdebebas, the second part of a potentially pivotal weekend in the title race, after Barcelona meets Atleti on Sunday (AEST).
Atleti is two points clear of Real Madrid and Barca after it beat Elche, before Real Madrid saw off Osasuna and Barcelona edged out Valencia.
Sevilla had been the form team at the top, having won five games in a row, but its chances of overhauling the top three now look slim.
It will surely have to beat Real Madrid next weekend to reignite its hopes, before finishing the season at home to Valencia, away at Villarreal and at home to Alaves.
Williams held his nerve at the crucial moment, sent clear after Oihan Sancet had torn away on the break before slipping left to his team-mate.
With Sevilla's Fernando pulled across, Williams had time to pick his spot, opening up his right foot and lifting the ball into the right-hand corner.