Babcock and Matthews have not always seen eye to eye, whether it was over linemates, ice time or style of play. The coach visited the 21-year-old at his Arizona home last offseason; they had a discussion Babcock described at the time as "productive."
Matthews seems to have bought what the coach is selling and is poised to take the next step in his game, much like his team. By concentrating more on defense, he has started to notice tangible results on the score sheet.
"I think that's been huge for me," Matthews said. "Tonight I thought all five guys, we were working as a five-man unit, breaking out clean. Just be in a good spot for the [defensemen] and communicating. That's the biggest thing, letting them know you're there and you're in a spot where they can get you the puck.
"I know for myself, I want the puck as much as possible. If you're in a good position and getting it and moving it, it gets us all going and we're playing in the offensive zone."
The next stage of the learning curve for Matthews and his teammates is to finish off the Bruins on Sunday. Returning to Boston for Game 7 on Tuesday is a something they want to avoid.
"Obviously, the hardest game to win is the fourth game to put the other team out, especially a proud group of guys," Babcock said. "It is something that we haven't been able to do in the last three years. I don't think we even should've been in the playoffs two or three years ago, but we got there. Now it is the process of learning how to do this. That is all a part of growing the group.
"It's not easy, as you can see in the League. It's not easy. We will get prepared to really push."
A push that Matthews appears ready to lead.