Perth threatened to complete a monumental comeback before Brisbane, after a blistering start, steadied for a 109-104 NBL win.
The Bullets led by 24 points midway through the third term at home in Wednesday's Ignite Cup after piling on 63 first-half points.
But the Wildcats woke up and, with influential Bullets guard Raul Neto (10 points, eight rebounds) off the floor seemingly nursing a leg concern, three quick triples from Kristian Doolittle made it a two-point game with five minutes to play.
Back-to-back triples from Taine Murray (14 points) steadied the hosts though as they stayed more than one possession clear in the final minutes to avoid what would have been a deflating loss.
It moved the Bullets, who only won six games last season, to 6-5 under new coach Will Weaver, while the Wildcats are now 5-5.
Neto had earlier put the Wildcats in a spin, his no-look backhand flick assist to Tyrell Harrison (16 points, five rebounds) a highlight of a brilliant first half that came on the back of a last-start victory in Adelaide.
Nate Hinton (13 points, eight rebounds, four assists) was big at both ends as the Bullets threatened to break records, only for John Rillie's side to claw back
Doolittle barely fired a shot in the first half before exploding down the stretch to finish with a game-high 24 points and nine assists, while Anthony Dell-Orso (20 points) and Elijah Pepper (19 points) also got going.
Mitch Norton (13 points, four rebounds, three assists) attempted to steady the ship with Neto, on the roster until Lithuanian guard Arnas Velicka returns from injury next month, on the bench.
Lat Mayen (14 points) made a difference for the Bullets off the bench, hitting shots in the first quarter to get the hosts going and then all but sealing the contest with another triple inside the final minute.
The Bullets, while improving to 1-2 in Ignite Cup, lost both of the final two quarters to the Wildcats to take five of a possible seven points from the clash and all but dash their hopes of featuring in the in-season competition's final.