Sevilla are unbeaten in six league matches since a 4-0 thrashing at Barcelona last month and trail the reigning champions and Real Madrid by only one point, although they have played a game more.
A tight encounter was settled by the only goal in the 13th minute, as Javi Moyano brought down former Manchester City winger Nolito and Argentinian international Banega dispatched the resulting spot-kick.
Lucas Ocampos of Sevilla was sent off late on after receiving a second yellow card for time wasting, but the visitors held on to continue their excellent start to the season under former Spain and Real Madrid coach Lopetegui.
Barcelona lead the table on goal difference ahead of Real Madrid after beating Leganes on Saturday.
Earlier on Sunday, substitute Kenan Kodro scored a late winner as Athletic Bilbao claimed a 2-1 victory at Osasuna to move fifth.