Two quick-fire tries and yellow card to Josh Drauniniu had Warriors rocking and fans fearing the worst.
But the home side dug deep and further scores from Blair Cowan and Jonny Arr ensured it was all smiles and maximum points at Sixways.
"The key to stopping Wasps was to halt Ashley Johnson, to cut the lifeline to the wingers and to make sure if we lost a turnover we didn't fly out of the line and kept our shape," said Hill.
"All three were good in the first half. Our discipline was also good as we had conceded four and they had conceded six.
"I told the players to go out and show the Worcester public what we could do in attack and we scored two great first half tries.
"At half-time we had done what we needed to do. But the first ten minutes of the second half was incredible, I thought we were going to shoot ourselves in the foot again.
"We made silly errors. It wasn't panic, but you could almost sense that Wasps were getting momentum.
"The way the players steeled themselves to come back from a tricky situation was impressive, because I was sat there thinking 'this is not going well'. We showed the self-belief to pull themselves back together again.
"I thought we came back well and that was good going. You could see it slipping away and it was testament to the character of the players.
"They are developing a confidence and they have had a few knocks this year that they probably didn't deserve when losing games at the end."
Hill also paid tribute to Danny Gray, as he climbed off the bench to step into the shoes of Andy Goode and lead Worcester home, and a fearless display from scrum half Jonny Arr who also came off late on after putting his body on the line.
He said: "Andy has had a dead leg. He picked it up against Gloucester and hasn't trained all week.
"He said he was okay and played the first half and did some good things, but clearly it wasn't right and it got a bit messy at the start of the second half.
"We brought Danny Gray on and he stepped up to it. It was a little bit scary when he missed the kick in front of the posts, but he didn't let it affect him and he hit some superb line kicks into the corner to get out lineout going.
"I was pleased for him, it was a big stage and very important game for him to step up like that.
"Jonny really put his body on the line like he normally does. He is not the biggest of blokes but he absolutely gives 100 per cent in terms of physical commitment. He took a bit of a knock so we took him off late on."