Perhaps unsurprisingly, after a difficult second half of 2009, Everton are keen to see good omens in a winning start to 2010, even in the wake of a result that left them feeling a little sorry for Carlisle.
"The scoreline totally flattered us," their captain, Phil Neville, conceded, after a Tim Cahill goal with eight minutes left, followed by a stoppage-time penalty, had turned 1-1 into 3-1.
Those thoughts were echoed by his manager, David Moyes, who has found optimism hard to maintain over the last few months, during which the Premier League form of an injury-hit squad has faltered badly. "I cannot be disappointed with the result," he said. "We had nine players injured and two away at the African Nations Cup, plus one suspended," Moyes said.
Set up to mirror Everton, Carlisle conceded an early goal when James Vaughan intercepted Adam Clayton's backpass but equalised quickly when Clayton's shot, half-saved by Howard, was helped over the line by Kevan Hurst. Thereafter, they held their own with Clayton, 20, and Tom Taiwo, 19, the game's brightest players.
If there was a turning point, it came when Everton keeper Tim Howard's fingertip touch on Danny Livesey's 71st-minute volley sent the ball ricocheting fortuitously into the crossbar, narrowly preventing Carlisle taking a 2-1 lead.
Carlisle deserved a replay but, with eight minutes left, referee Jon Moss allowed Everton substitute Seamus Coleman the benefit of the doubt when he barged roughly past Matt Robson and the defender's cross resulted in an opportunistic goal for Cahill. A foul by goalkeeper Adam Collin on substitute striker Keiran Agard then allowed Leighton Baines to give the scoreline a misleading look.
Everton (4-2-3-1): Howard; Hibbert (Coleman, 80), Heitinga, Neill, Baines; Neville, Fellaini; Bilyaletdinov, Cahill, Pienaar; Vaughan (Agard, 86). Substitutes nut used: Nash (gk), Duffy, Forshaw, Baxter, Mustafi.
Carlisle United (4-2-3-1): Collin; Keogh, Livesey, Harte, Horwood; Clayton, Taiwo; Hurst, Kavanagh (Anyinsah, 85), Robson; Pericard (Dobie, 77). Substitutes not used: Ridgeley (gk), Bridge-Wilkinson, Murphy, Burns, Kane.
Referee: J Moss (W Yorkshire).
Bookings: Everton Fellaini, Neville; Carlisle: Collin.
Man of the match: Taiwo.