Cecil Corbett and Johnny Black were also on target in front of a bumper crowd at Madden Road as Rovers proved too strong for St Mary’s.
Rovers had an early penalty shout dismissed during sustained possession across the opening period, with Iain Latimer close with headers off two corner-kick plays.
Bicker sparked the semi-final into life by collecting an upfield punt from his goalkeeper, Richard McGivern. Bicker flicked the ball over his marker then smashed home a volley from distance.
Luke Carvill had a sight of goal for the Saints but Rovers held control at half-time.
Corbett marked his introduction off the sidelines by heading home a Bicker delivery before the latter attacked from deep and capped his run with a superb long-range shot.
Philip Pedlow had a drive from distance bounce off the crossbar and Lee Wells fired just past the post before Rovers made it 4-0 thanks to Johnny Black’s fine turn and finish.
“We discussed before the match how Tandragee Rovers sit as the benchmark for our level,” said St Mary’s Gerry Fay. “They have the big-game experience, impressive fitness levels and move the ball so quickly.
“We sit in a rebuilding process so will learn from the semi-final.”
TANDRAGEE ROVERS: Richard McGivern, Philip Pedlow, Jamie Rooney, Colin Bingham, Gary Whiteside, Iain Latimer, Lee Wells, AJ Gallagher, Mark Bicker, Johnny Black, Simon McClean. Subs: Scott Walker, Dean McCammon, Jamie Uprichard, Gareth Dobbs, Cecil Corbett.
Tandragee will take on Camlough Rovers on February 27 in Armagh’s Holm Park.