But any momentum that slipped Hamilton's way was erased by Tyrvainen just more than three minutes into the second period.
He blocked a shot, then raced past the shooter as the puck bounded across the blue line.
House charged up the opposite side but after faking a move to the trailer, Tyrvainen buried it past Peter Delmas to put the Barons ahead.
Hunter Tremblay gave the Barons some breathing room midway through the third with his 15th goal of the season, and Ryan Keller added an empty-net goal as time wound down.
David LeNeveu stopped all 30 Hamilton shots to record his second shutout of the season.
“He's been in a tough situation sometimes lately getting the third in three, playing when everybody's tired in front of him,” Tremblay said. “We hung him out today a few times but he came up big for us.
“It's nice to give him a game where we'll all fresh.”
The Barons host Peoria at 7 p.m. Friday in the second of a four-game homestand.