Coach Mack can coach
It wasn't apparent in the first half, as DePaul came out with an incredibly predictable barrage from deep and looked at times like they were going to bury the game (see below). Out of the half, though, Xavier defended like maniacs, attacked the basket on offense, and put together a 26-10 run in the first 7:47 after the DePaul free throws before the half began. You can't come flat out of the half if you're down big, and Xavier definitely didn't.
If you can shoot, you can score on Xavier
DePaul was 18-30/11-19/1-2 shooting in the first half. They cooled off considerably in the second half, but they still got some good looks at the rim from behind the arc. Xavier did what they needed to do to claw back at home, but the person who still worries about Xavier's defense is probably not being overly pessimistic. You play like this against, say, Villanova, and you're not coming back.
Matt Stainbrook is kind of a big deal
Xavier's game turned around when Coach Mack went to four small around Matt Stainbrook. You can get away with this a big against DePaul because they don't have true post scorers on the other end, but having Stainbrook to run the offense through inside was a huge part of Xavier's success in the second half. The ability to go inside out opened up spaces for players to drive into DePaul's defense, which led to the points that brought Xavier back into the game.