Brian Jefferson and Ahmaad Wilson had most of the steals for Randallstown in the fourth quarter.
The Rams remained composed at the free-throw line, making 10 foul shots down the stretch and 21 of 25 for the game.
Wilson finished with a game-high 17points.
No. 7 archbishop Spalding 80, No. 3 John Carroll 71: The host Cavaliers (17-7, 10-3 Maryland Interscholastic Athletic Association A Conference) bounced back from a three-point loss to the Patriots (21-8, 9-5) on Monday.
No. 4 Mount St. Joseph 71, Glenelg Country School 68, OT: The host Dragons (9-14, 4-9 MIAA A Conference) dominated the paint in the second half to force overtime, but the Gaels (20-5, 7-3) outscored them 12-9 in the extra period.
Kameron Williams had a game-high 27points for Mount St. Joseph. Warren Powers finished with 19 points for Glenelg.
No. 11 Boys' Latin 65, Gilman 60: Colin Heacock scored 16 points for the Lakers (18-3, 13-0 B Conference) to keep the Greyhounds (11-12, 7-6) at bay.
No. 12 Oakland Mills 57, Reservoir 51: Senior Lavon Long stepped up again, scoring a game-high 20points to keep the Scorpions unbeaten.
Oakland Mills improved to 16-0, 13-0 and the Gators fell to 7-5, 6-4.