A late penalty from Ceri Sweeney appeared to snatch the win for Cardiff but with the final play scrum half Ollie Frost dotted down for a deserved victory.
Worcester scored three tries but could have scored many more as they showed real attacking verve and threat to the delight of boss Hill.
He said: "I saw us put together some very good attack and that is very pleasing.
"We have been working on that for the last three or four weeks. We wanted to see some evidence of the work we have done with Mathieu Rourre on the attack and for me that is what we showed. I was very pleased by that aspect.
"We had a lot of good shape in attack, huge enthusiasm and we made an exceptionally high number of line breaks.
"We didn't finish them off on occasions, which is a negative, but I saw enough today, and the players did, to prove the work we are doing on the training park is translating to the game.
"Yes, we could have scored more. Some of it was two-on-one execution, the final pass or the ball was dropped. We were offloading at the wrong time and spilt ball at crucial situations.
"But we have got to look at those line breaks as a big positive. If we can do that more and finish them off, we had people flooding through to support them, then it bodes well."
Hill was also pleased to record a win on the road as Warriors look to back up Fortress Sixways this season with more points on their travels.
"We came here with the intention of winning because it gives everybody a boost," added Hill. "As Dean Schofield said at the end in the huddle, it's an away win and we can build on that.
"Granted it was over a young Cardiff side, but we have got to get used to winning not just at home on a Friday night. We have got to be able to come away to the likes of Cardiff and get results.
"That will give us a big boost and there was enough there to work on. It's our first game, there were nerves and we needed to be calm which led to handling errors. But we can work on that.
"I was also pleased that at the end, when Cardiff got the penalty and looked like they had won it, we came back with one play to go and scored a try after several phases. Good old Frosty saved the day with a try under the posts and that shows great character.
"We're not getting carried away, there is much to work on, but we are pleased with a win in the opening game of pre-season."