The performance and result was a perfect response after a week of soul-searching following the Wigan loss.
It also ensured manager David Moyes would have something pleasing to mark the 11th anniversary of his appointment with.
Moyes said: "I would have been disappointed if we hadn't responded, and surprised if we hadn't.
"The players played great. We were playing the champions of England and I thought we gave them a right good run for their money.
"What you saw is what Everton do. I thought we played really well in the first half and I thought in the second half, when we were down to 10 men, we did what Everton did 11 years ago when I took over.
"We were resilient, hard to beat, made sure the opposition didn't score, threw ourselves on the line for the team.
"We were rubbish last week but we have been good all season and you are watching a really good Everton side.
"It is just to make sure people realise we have not gone away. We are still there. I think people last week thought we had gone away."