The 24-year-old, whose move from the Sydney Swans was the last deal completed in last year's trade period, made his mark early, snaring two majors in the first quarter.
He split his time between attack and defence during the rest of the game, which Carlton won 1.14.7 (100) to 0.14.9 (93), taking a couple of strong contested marks down back and finishing with 17 possessions to go with his three goals.
"He had a good game, and he's fitted in very well at the football club," Blues coach Mick Malthouse said.
"The boys like him. He's a pretty quiet type, he's made friends, and I think the best thing to come out of today for him is that he's able to play in multiple positions.
"So he'll become a valuable player, I'm sure."
Everitt's performance was among the high points of a vibrant effort from the Blues, who went into the game without a host of senior players, including Chris Judd, Kade Simpson, Matthew Kreuzer, Lachie Henderson, Heath Scotland, Jeff Garlett, Michael Jamison, Andrew Carrazzo and star recruit Dale Thomas.
Midfield general Brock McLean took up from where he left off last season, gathering 21 touches, while Ed Curnow and Andrew Walker also won plenty of the ball.
Despite fielding what looked to be an almost full-strength side (they were missing only Liam Anthony, Andrew Swallow, Leigh Adams, Nathan Grima and Robbie Tarrant from their best team), the Kangaroos were lacklustre in the opening half.
But they burst into life midway through the third quarter, booting six goals to one and narrowing the margin to one point by the 24-minute mark of the final term, before being unable to land the finishing blow.
Brad Scott's men dominated the possession-count, finishing with 376 to 301, but were less efficient than their opponents.
Star recruit Nick Dal Santo was among the major ball-winners for North, while fellow midfielders Ryan Bastinac, Jack Ziebell (game-high 147 Fantasy points) and Daniel Wells showed plenty of encouraging signs.
Veteran key forward Drew Petrie, who enjoyed an entertaining battle with Carlton's Sam Rowe, delighted his home crowd by kicking four goals.
?WHAT WE LEARNED
The loss of Eddie Betts hasn't dampened the Blues' scoring power. Even with Jarrad Waite struggling to get a kick, Mick Malthouse's men piled on nine goals in a great opening half, with recruit Andrejs Everitt and star youngster Troy Menzel bagging five between them. Tom Bell (87 Fantasy points – the highest score of any Carlton player) also showed plenty of verve in attack and in the middle.
NEW FACES
Andrejs Everitt was the standout new-boy for the Blues, although draftee Patrick Cripps and former Collingwood ruckman Cameron Wood also caught the eye a few times. Cripps, a solidly built midfielder, finished with 12 possessions and three clearances. Working in tandem with Robert Warnock, Wood didn't win many possessions around the ground but he tallied 19 hit-outs. And he delighted his new fans by slotting the last goal of the game, which ensured Carlton was able to put a stop to North's frenetic fightback.
NORTH MELBOURNE 0.2.3 0.9.3 0.9.9 0.14.9 (93)
CARLTON 0.3.3 0.5.6 1.12.5 1.14.7 (100)
SUPERGOALS
North Melbourne: Nil
Carlton: Tuohy
GOALS
North Melbourne: Petrie 4, Black 2, Thomas 2, Harvey 2, Currie, Wells, Ziebell, Bastinac
Carlton: Everitt 3, Menzel 2, Ellard 2, Bell 2, Cachia, Robinson McLean, Wood, Casboult
BEST
North Melbourne: Bastinac, Ziebell, Petrie, Dal Santo, Wells, McDonald, Tippett
Carlton: McLean, Curnow, Everitt, Robinson, Buckley, Bell, Cachia
INJURIES
North Melbourne: Nil
Carlton: Nil
Reports: Nil
