Whitburn hit the woodwork three times before taking the lead on the half hour when Scott Meldrum sent over a perfect cross for Barry Craig to head home from ten yards.
Into the second half and again they hit the woodwork before doubling their lead. This time the ball came down the left with Jordan Swan creating the chance. He cut the ball back on the byline leaving an easy tap in from Michael Brown.
The hosts did grab a goal back when Sam Muirhead glanced a header out of Francis Carlin’s hands but, it was a little too late to mount any serious challenge to a solid Whitburn defence. Whitburn then ran the clock down for in the end a comfortable win.
Meanwhile, Armadale were beaten 2-0 by Kilsyth in a third-round replay of the Junior Cup.
Glentanar: McLennan, Dines, Morrison, Rennie, Scott, Gray, Spalding, Shanks, Munro, S Muirhead, Workman. Subs: J Muirhead, Adams, Perfect, Rainnie, Asken, Taft, Antanassi.
Whitburn: Carlin, Gordon, McDonald, Woodhouse, Mooney, Spence, Meldrum, Brown, Craig, King, Swan. Subs: Wilson, Young, Taylor, Bucknell, Sharp, Ritchie.