It's called time, and that's why Tomori was successful. She waited for Yuu to get some distance from Ayumi's death, all the while making sure he doesn't kill or ruin himself completely (the drug kicking scene established this).
Yuu isn't dumb. He knows what he is doing is wrong and that he is running away. He just didn't have the leeway to stop by himself earlier. Knowing that someone was willing to sacrifice/do so much for him (established by his imagined flashback of Tomori always being around) gave him a shock, enough to knock some sense back into him. Then all it took was Tomori baiting him with the promise of leaving him alone and poisoning him with sweet sauce.
It's quite common for those in a downward spiral to hit rock bottom before climbing back up. That's what happened here.
I'm not even speaking hypothetically. I can empathize really well with Yuu because of firsthand experience.
EDIT: To put things into perspective, Tomori took a leave of absence from school and consequently stopped looking for power-users (which was practically her raison detre) while she was silently watching Yuu. Ex-GF went on one visit, got turned away, and never came back. Glasses and idol visited as far as his door a couple of times, and that's all they did. Tomori put everything on hold to watch over him, and in the end actually did stop him from ruining himself with drugs.
Having experienced a similar loss, she knew half-baked words and charity visits won't help. She knew what to do based on experience. Her tolerance for violence and danger was a bit extreme, but that's always been part of her personality.