In a close-fought game, Lealholm proved to be the slightly better side.
The home side took the lead after just five minutes – some good work from Morgan saw him put the ball into the box for Brown to shoot home.
Ten minutes later, Brown claimed a slightly fortunate second when the ball was passed back to the Redcar keeper who kicked it out, only for the ball to hit Brown on the back and bounce into the net.
But Lealholm got complacent and allowed Redcar to get back into the game with a goal five minutes before half-time.
Fifteen minutes into the second half, Lealholm increased their lead.
Morgan's first effort was well saved but the rebound fell kindly for him to produce an overhead kick into the net.
Ten minutes later a well worked move down the left saw Redcar pull a goal back to set up a tense finale.
The last 10 minutes saw neither side create any scoring chances and Lealholm now play FC Bull's Head on Friday 2 May at the Turnbull.
Results: Lealholm 3 Redcar Rugby Club 2