Holland scored the eventual game-winning goal in the fourth round of the shootout, out-waiting Pickard with a series of dekes and sliding the puck through his five hole.
Andrew Agozzino attempted to level the shootout in the fifth round, but Mayer denied his wrist shot with a butterfly save to end the game.
Two penalties within the first five minutes for the Monsters gave the Bulldogs plenty of offensive zone time to work with early.
Despite generating shots, Hamilton was unable to craft a convincing scoring chance over the course of four minutes with the man advantage.
The game's first goal fell instead to the Monsters on a broken play at 8:13 of the first period.
Colin Smith slid the puck cross ice from a bad angle and Mayer kicked the pass-turned-shot to his left, and straight to Schumacher in the low slot. He easily slotted the puck past the downed Mayer in tight.
Neither team generated much pressure as the period wore on, until Hamilton established its forecheck to create an equalizing goal at 17:31.
Maxime Macenauer took control of the puck behind the Lake Erie net and found Andrighetto to the left of the slot. The Bulldog winger quickly snapped a wrist shot up and over the shoulder of Pickard at the near post from a bad angle.
There were few chances to be had in the second period, much like the first before it, but Hamilton capitalized on one of the few to take the lead at 16:08.
The combination of Justin Courtnall and Nathan Beaulieu wove through the Lake Erie zone, eventually teeing the puck up for Pateryn, who waited and fired a slap shot through a thick screen and past Pickard.
Lake Erie struck back to level the game once again at 7:37 of the third, when Elliot drifted in from his post at the point.
Mitch Heard cycled the puck to Garrett Meurs to the right of Mayer's net, and the winger sent a long centring pass to Elliot at the blue-line, who walked in to the top of the circle and fired a shot through traffic that beat Mayer inside the far post.
Overtime solved nothing, although Hamilton's Mike Blunden came closest to ending the game when he found himself alone in front of Pickard, but lost the handle on the puck.