Toronto came out fast and found itself ahead 2-0 less than three minutes into the game.
Johnsson opened the scoring on a breakaway with his team-leading eighth post-season goal at 1:32, and it took only 47 seconds for Moore to double the lead when he put back a rebound in front of McKenna.
Bayreuther put some energy into the home-crowd at HEB Center when he beat Sparks 4:06 into the second, but Greening and Rosen responded with goals 1:07 apart to make it 4-1 at the 8:45 mark.
Rosen added is second of the game at 17:07 for a four-goal advantage after 40 minutes.
Grundstrom and Dries traded goals 15 seconds apart midway through the third with the game out of reach. Texas thought it added a third goal late in the period, but it was called off because of a high stick.
Game 7, if needed, would be Thursday at Ricoh Coliseum as the best-of-seven series follows a 2-3-2 format.