Baines recovered after being fouled by Ashley Williams to curl a lovely free-kick beyond Michel Vorm just before the hour mark, and Jelavic sealed the win by tapping in his second goal for the Toffees with 14 minutes remaining.
Swansea had dominated possession during the opening half, but could not make it pay as Gylfi Sigurdsson and Danny Graham failed to convert their best chances.
Source: PA
Source: PA