Hill pinpointed the flying start as crucial as Worcester soared into a 24-0 lead in only 24 minutes as prop ace Black came to the fore to grab his first tries for Warriors.
However, he admitted it needed power off the bench to finally overcome a stubborn and determined Moseley side that shut Worcester out for almost 50 minutes before a three-try burst in the final minutes ended the resistance.
Hill said: "It was a pleasing victory - good start and good finish, maybe we went a little quiet in the middle patch. But it was nice to finish with three tries.
"I was pleased about the start because we have had a job to get off to a good start in a lot of our games.
"We didn't put a foot wrong, we were catching restarts, the handling was strong and we produced clinical rugby without making an error for 24 minutes.
"At 24-0 after 24 minutes it was a really good start and you thought Moseley might crack at that stage but, to their credit, they really stuck in there, made life hard for us and played some good rugby.
"We got sloppy at the end of the first half. It was a little natural as we had scored three tries and players were trying to force it for the fourth bonus point score, trying to offload the ball in difficult conditions and it wasn't really working.
"We lost a little bit of our directness so the message at half-time was to tighten up. I was pleased at 24-7 at the break but not totally, we had dropped a few high balls and got a bit sloppy."
Winger Benjamin finally ended any anxiety at Sixways with his 11th try of the season and Hill was pleased with the impact of his replacements in the final quarter.
"The first quarter of an hour in the second half was about getting a firm grip again and control, then bringing the replacements on. But even in that period Moseley made life hard for us and we had to wait longer until we got that vital fourth try, it was getting a little nerve wracking towards the end," he added.
"We needed that extra try and we scored a good one, then we relaxed and grabbed a few more.
"There had been a spell when Moseley put us under pressure and our forwards found it hard work, they were flagging a little bit.
"But that is the advantage we have over other teams, our replacements are quality and I thought Jonny Arr added an injection of pace, Dale Rasmussen looked strong and the front row, with Chris Fortey and Bruce Douglas coming on, gave us a new lease of life."