"We needed a run to get it over with," Brown said of the strong second-quarter finish.
Clinging to a one-point lead, the Wildcats (27-1) ended the second quarter on a 13-0 push to go up 34-20 at the half.
Brown started the surge with the one-handed slam, but it was only the beginning as the Hornets also committed a few turnovers during the run.
Laney's Raheem Newton added two free throws and a Rod Hall layup followed by a Brown 3-pointer soon stretched the Wildcats' advantage to double figures. Brown scored nine of his 12 first-half points in the second quarter. He finished with a game-high 17 points as Laney, the No. 2 seed from Region 3-AA, advanced.
The second-period run came after a mostly even first half, with Cook keeping pace with its zone defense.
The Hornets took an early 10-6 edge on a Jerome Hill slam.
But Laney soon took advantage of the free-throw shooting discrepancies. The Wildcats made 10 more made foul shots than their opponent in the first half to take a 14-point advantage into halftime.
The Hornets threatened the Laney lead in the third, cutting it to 40-31.
The game might have been closer had Cook not gone through a 1 for 5 stretch at the line in the period.
Up 10 points heading into the final quarter, Laney began bleeding the clock. With Cook backing off, the Wildcats simply held the ball during a few possessions as the pace slowed.
By the time Hornets coach Tommy Blackshear told his team to match up defensively, there was about 4:30 left with the Laney lead still 10.
Blackshear said he liked his squad's chance to rally had the Wildcats not slowed down the pace of the game.
However, the Hornets' only point in the fourth came on a Quinton Fletcher free throw with 3:23 remaining as Laney's lead ballooned to 19 thanks to some strong defensive stands, with a few blocks and strips halting scoring chances.
Laney coach Jerry Hunter pointed to defense as the key to winning in the state championship.
A Jamie West steal and two late Hall dunks capped the victory. The teams combined to score only 29 points in the second half.
"It's all about advancing," Hunter said.