Klitschko basically tried to destroy Brewster from the opening bell and never let up until he punched himself out. He was very, very aggressive and never stopped thowing power punches. He almost had Brewster out in the 4th, but instead of slowing the pace and cruising to an easy victory or late stoppage, he punched and punched and punched until he didn't have anything left. He showed in the rematch that he wasn't going to make the same mistake again.
He threw like 300 punches in 5 rounds with as much force as possible. And when you're 6'6, 245 pounds you're gonna hit a wall and that's exactly what happened. It also doesn't help that Wlad is one of the least relaxed fighters in the ring.
Klitschko had a high volume of punches in the first Brewster fight and for some reason his corner man decided to frost him with vaseline :huh which probably did way more harm than good.