Goals from Rayan, Marcus Tavernier and Evanilson ensured the Cherries celebrated their 350th Premier League appearance in style.
The victory also extended the club's impressive defensive run to four consecutive clean sheets across the Premier League and Europa League.
“It was a really special performance. Coming here and getting three points is hard for any team,” Hill told the club website.
“But for us to come here and keep a clean sheet as well and score the three goals, credit to all the team today, they were brilliant.
“They’re in a difficult position but we didn’t focus on that, we focussed on putting a good performance in. We focussed on ourselves coming into a massive fixture against a team with a lot of quality.
“We’ve been really good recently and we’re pleased with our clean sheets recently. We were outstanding to a man.
“We have had lots of games recently but we wouldn’t want it any other way, it’s been an incredible journey.”