The third-round victory came at a vital time for the Blues, stopping a worrying trend of six consecutive fixtures without a win, including shipping 12 goals in their previous four games without finding the net themselves.
Oumar Niasse was the hero for Ronald Koeman's charges as he came off the bench just before the hour and struck a brace to cancel out Joshua King's 49th-minute opener. Updates are sent twice a week. Today it was Bournemouth who got the short end of the stick, and this result sees them on a meagre three points, sitting in 19th.
He has not played a game since picking up a knee injury in the 3-2 Premier League defeat to Spurs last March, while his appearances for his country last October led to a war of words between Everton and Ireland team management.
Bournemouth boss Howe could scarcely believe his eyes when Romelu Lukaku thrashed home the first of a personal four-goal haul after only 30 seconds - equalling Chelsea's Pedro as scorer of the season's fastest goal in the process. We still have a lot of work to do.
Everton have just two wins in their last 10 league matches, registering four goals.
His £75m move to Manchester United has clearly hit Everton hard and they weren't been able to score in any of the past 4 games in all completions.
Calvert-Lewin produced the Toffees' first goal since August 24 with a cool finish in the 38th minute before adding another composed strike six minutes after the break. In the Premier League, you can't give yourself a mountain to climb and you can't start so badly that you are in a position where you are playing catch-up because it is such a tough league.
Routed 6-3 at Everton last season, Bournemouth were on the back foot again as Gylfi Sigurdsson appealed in vain for an early penalty after tumbling under pressure from Dan Gosling.
Rooney has won all 11 league matches in which he has scored at Goodison Park - eight for Everton and three for Manchester United.
Bournemouth's Simon Francis, centre right, collides with Everton's Wayne Rooney, during the English Premier League soccer match between Everton and Bournemouth, at Goodison Park, Liverpool, England, Saturday Sept. 23, 2017.
Visitors Bournemouth could well keep faith with the side that beat Brighton in the Premier League last weekend.
Probability of away win: 17%.