The 21-year-old headed the hosts into a 26th-minute lead and then sealed matters with a late header as Gus Poyet's side posted back-to-back wins for the first time in almost three months.
Wickham was also involved in the second goal when Sunderland won a penalty when Juan Cala was sent off for tugging back the striker as he tried to race clear on goal.
Despite playing against 10 men, Wickham believes Sunderland were worthy winners.
"It's never easy against these teams, even when they've got 10 men," Wickham told Sky Sports News. "But we had a job to do and we're on our way back now.
"I don't really feel the pressure, to be honest. We created chances a hell of a lot over the last few games. We deserved that result. We're doing what we can do.
"The team performed well today. We created a lot of chances and defended right from the back from the goalkeeper all the way through to the forwards so I think we deserved what we got today."
Wickham also backed referee Phil Dowd's decision to send off Cala and give Sunderland a penalty for the foul on him right on the stroke of half-time.
"Obviously I felt he pulled me down," added Wickham.
"I felt I could have scored. If you go down, he's going to get sent off, but I felt I could score. But he (referee Phil Dowd) brought it back and I think he made the right decision."