The Mariners staged a thrilling comeback from two goals down to defeat the same opponents 3-2 the last time these sides met in February, but a resurgent City made no such mistake in rainy conditions this time.
Maclaren opened the scoring with his eighth goal in his past five appearances, coolly slotting into the right-hand side of the goal from Florin Berenguer's tee-up at AAMI Park.
That was the in-form striker's eighth goal in his past four matches against the Mariners, and only the form of visiting goalkeeper Mark Birighitti denied Adrian Luna and then Maclaren from extending City's lead.
Atkinson's second A-League goal put City in command after 56 minutes, the full-back finishing from a tight angle after Andrew Nabbout's original shot deflected into his path.
Maclaren had another great opportunity to extend the lead but his point-blank header was saved by Birighitti.
City is now fourth in the standings, only four points back of the Mariners with two games in hand on its table-topping opponent.