Ings struck in the first half, his seventh league goal of the season, before Vokes doubled the hosts' advantage with his fifth in four Championship games late on.
Jason Shackell's own goal with eight minutes remaining set nerves jangling at Turf Moor, but the Clarets held on to earn their fifth league win in a row which represents their best start to a season since 1961 - when they finished runners-up in the top flight.
"I thought we were absolutely excellent," said Dyche. "We created many chances and we looked solid and their keeper had to be on form.
"We are still a work in progress but we went into the game with a good focus and we produced a really good performance.
"We showed we can compete against everyone and we are in a magnificent position to do that in every game we play.
"This was up there with our best performances of the season and we are on a roll, but it doesn't guarantee you anything.
"Reading have very good players, but we shifted the ball well, kept it well, our framework was good and all the things you look for as a manager were delivered.
"They scored a goal out of nothing, but we closed the game out in a professional way and the players gave maximum effort. The back four were nice and solid and we had a great ethic."
- Sports & Recreation
- Sam Vokes
- Danny Ings
- Jason Shackell