Tries from full-back Chris Pennell, wing David Lemi, number eight Blair Cowan and scrum-half Jonny Arr saw off Wasps 29-23 at Sixways and sent Worcester 13 points above bottom club Sale Sharks.
"There was a lack of crucial errors at crucial times by individuals," Hill said.
"There was a coming together of set-piece, attack and defence. All three areas were pretty good and you could see it in the players' eyes before the game that this was a game they were determined to win.
"It was about time all parts of our game came together and there was a real excitement in the team. The intent was there to try to score tries. Chris Pennell scored a marvellous try out wide and there was a little bit of magic from Andy Goode to chip over the top for David Lemi's try."
Goode chipped in with a penalty and conversion before going off nursing a leg injury, while his replacement Danny Gray added two conversions to nullify touchdowns by Wasps hooker Rhys Thomas, flanker Ashley Johnson and substitute Jack Wallace.
Wasps, in fifth place before kick-off, were left to ponder a second Premiership reversal of the week after they lost against London Irish last Sunday, despite fly-half Nicky Robinson keeping them in touch through two penalties and a conversion.
"We spoke at half-time that it was important to go out and score first and get ourselves back in the game," Wasps assistant coach Trevor Woodman said. "We managed that and we got our noses in front, and then there was a period of three penalties and they were suddenly camped on our five-metre line.
"We started the game strongly and then a lot of mistakes crept into our game up to half-time, but we played some good stuff in the second half. We looked very tired last weekend but there are no excuses. We didn't over-train the boys this week. I don't think there was tiredness out there, just a bit of sloppiness.
"But we finished strongly and made sure we came away with something in terms of a losing bonus point."
- Sports & Recreation
- David Lemi
- Chris Pennell