It took strikes from the Toffees' over-age players Arouna Kone, Bryan Oviedo and Conor McAleny to see off a determined visiting team, who scored through Liam Agnew and Carl Lawson in an entertaining contest.
Club legend Niall Quinn has praised the impact of goalkeeper Costel Pantilimon since coming into the fray, whilst also giving credit to Gus Poyet for Sunderland's recent improvement.
Quinn believes Sunderland were at a crossroads following the debacle at Southampton, but have since shown great resilience to bounce back strongly.
"I see the majority of games and I have been impressed by the way they've got back on track after Southampton," said the Irishman.
"Gus and his staff deserve a great deal of credit for that, because it could have been a slippery slope and hard to recover from.
"Arsenal was a tough one straight after, but I think it's fair to say they're back in business."
Winger Adam Johnson is relishing the prospect of facing his former club Manchester City on Wednesday evening.
Easington-born star Johnson made 97 appearances and scored 15 times for City during a period in which they won the Premier League title and an FA Cup trophy.
Now he's looking forward to trying to cause another upset against a side who've struggled at the Stadium of Light in recent years.