Silva and Jesus got on the score-sheet to ensure City kept their end of the bargain to remain within a chance of securing automatic qualification into the UEFA Champions League next season.
Manchester City will be on the prowl for three points to secure their Champions League spot as they host Leicester City on Saturday at the Etihad stadium.
Manchester City edged closer to cementing a top-four spot as they beat Crystal Palace 5-0 at the Etihad Stadium.
David Silva and John Stones remain doubtful as Manchester City visit the Riverside Stadium to take on Middlesbrough on Sunday
Four different Spanish goalscorers ensured that Julen Lopetegui's mean cruised to an easy 4-1 victory against Elia Levy's Israel at the Estadio El Molinon.
Manchester City's 3-1 win over the Catalan giants will go down as one of the most historic nights for the club and could be a victory that spurs the Citizens on in Europe.
Manchester City have reportedly set a deadline for the French defender to make up his mind about whether he wants to join Pep Guardiola in the Premier League next season.
His recent run of performances have excited former Brazilian forward Ronaldinho, who says he is one of the best in the world and manager Jurgen Klopp should build his team around the attacking midfielder.
Having lost out the opportunity to capitalise on the dropped points by league leaders Arsenal FC, Manchester City will be hoping to set things right against Crystal Palace on Saturday, with David Silva returning to the starting XI.
Everton FC travel to the City of Manchester Stadium with added confidence, after beating the home side 2-1 in the Capital One Cup, but the Citizens will be taking this game much more seriously as they welcome back two experienced members of the team in Yaya Toure and David Silva.