The Toffees have lost just one of their last six matches to maintain their chase for a European spot in sixth place.
Baines believes that his side's 1-0 win over Fulham last weekend typified their defensive resilience and took the pressure off a struggling strikeforce.
He told Sky Sports News: "We have not been conceding many goals at all lately.
"We've kept a few clean sheets on the bounce at Goodison and we probably could have got another couple of goals against Fulham. We didn't put them away but in the end we only needed the one but we created some chances.
"We have been playing well and there was good build-up to the goal and we had a couple of other moves which were similar which didn't quite have the finish."
David Moyes's side face a stiff test on Sunday when they face Merseyside rivals Liverpool at Anfield.