Thomas gave the Blues a 1-0 lead at 2:03 of the second period. Bouwmeester scored at 10:01 to make it 2-0, and Maroon scored 54 seconds later at 10:55 for a 3-0 lead.
Eichel's power-play goal at 17:25 of the second made it 3-1.
"Obviously, it's not an easy day for us in terms of traveling, getting here, and the schedule, but I think that as a group, we probably should've been a little more mature about the situation and just given ourselves a better chance to win," Eichel said.
O'Reilly scored at 13:47 of the third for a 4-1 lead.
"It was kind of nice to put the nail in the coffin," O'Reilly said. "That two-goal lead and kind of getting late there, it didn't solidify the win, but it just kind of as a team, we were like, 'OK, we got this here.' ... Finding a way to get a big goal like that to seal the deal, it felt really good."