The fifth-seeded Tigers took a 32-30 lead into the fourth period, but Melbourne, the tourney's fourth seed, kept chipping away.
The Katz finally passed Valley Springs, 36-34, on a pair of free throws from Lee Lewis with a shade under five minutes left in the game.
Valley Springs then reeled off six straight points to move back in front, 40-36.
Chase Massey drilled a trey with three ticks left on the clock, but that was as close as Melbourne would get, and Valley Springs won 42-40.
A quick start helped the Tigers grab control of the affair early.
Valley Springs led 11-7 after one and then upped its lead to 20-9 in the second period.
However, Melbourne peeled off seven consecutive points to pull within 23-16 at the break.
Spencer Caraway paced the Bearkatz with 16 points, with Lee Lewis adding 13. Massey had eight and Dalton Grigg three for Melbourne.
The Bearkatz opened tourney play with a 67-53 win over Mt. Judea Jan. 5.
Melbourne led 15-5 after the first period and 35-14 at the halftime break.
Spencer Caraway paced the Katz with 15 points, while Grigg hit for 13 and Massey 10. Kody Caraway added seven, with Sam Cooper and Matt Loggains logging six points each. Lewis and Baird had five points apiece.