Hill confirmed skipper Matt Salter touched down for the first of his team's two tries after the pack drove Saracens over the line and left everyone in the ground bemused as to who actually scored among the pile of bodies.
But there was no question about who grounded the other as excellent full-back Luke Arscott beat the defence to touch down.
It was a much better display than their 27-0 defeat at Gloucester and Hill admitted as much, saying: "We looked fresh both physically and mentally today (Sunday).
"I did say after Gloucester that it was tough because we can't do it week in and week out. We had two huge games against Quins in the Heineken Cup and then a big game here against Wasps.
"We created a lot of holes and should have scored two or three more tries. We snuffed out their threats and I was really pleased with that.
"It was a really good balance. It was not all forward-dominated or all kicking. It wasn't just headless running. Watching that, I was more pleased than I have been for a long time."
The homework also helped snuff out the threat of Saracens scrum-half Neil De Kock and fly-half Glen Jackson.
Hill added: "We know their attack rolls around De Kock and Jackson. If those two are playing (well), Saracens function; if they don't, Saracens don't function.
"It was about closing those two down and I thought every time De Kock ran across the field in the first-half, he was smashed, and every time Jackson tried to show-and-go, he was dumped."
Saracens director of rugby Alan Gaffney was disappointed with the loss and admitted Bristol were the better side.
However, the Australian felt there was nothing to worry about despite the defeat being his side's second in successive weekends after losing to Newcastle at Vicarage Road last Sunday.
Gaffney said: "We won't be throwing the baby out with the bath water quite yet. We won't be changing much. We've just got to get to where we want to be - and we haven't been there for the last two weeks.
"That's been the problem. If we played the way we want to play then things may have been different.
"We came here confident of doing well and it was always going to be tough coming down the Memorial Stadium. We drew here last year and were pretty lucky to get away with that.
"Bristol play a very hard blitz defence so that did not come as any surprise. We have handled that defensive pattern in the past against Bristol and Wasps.
"I won't say it does not present you with any problems but you have to learn how to handle it and we didn't."