Evans (pictured) opened the scoring on 21 minutes at Goodison Park. After being fouled, he curled the resulting free-kick into the top corner of the net.
Ouzounidis headed in Everton's second from Conor Grant's free-kick in the 76th minute, ending Swansea's eight-match unbeaten run.
The win meant Everton replaced Swansea in fourth position, seven points behind leaders Leicester City with two matches in hand.
Everton: 11 Mar v Sunderland (A) PL2
Swansea: 12 Mar v Leicester (H) PL2