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The Clarets didn't win away from home last season until their penultimate road trip but led the champions 30 at half-time after the Londoners had skipper Gary Cahill sent off in the 14th minute.
Burnley's form at home and away contrasted sharply last season.
Dyche's side won 10 games at home - more than Manchester United and the ninth-best in the league - but managed only a solitary away win, at Crystal Palace. And their seven points on the road was the second-worst record in the league.
"A lot was made of our away form last season, and don’t get me wrong, that doesn’t correct it. But it’s a great start," said Dyche.
"It kills all the stories off immediately by getting a first win, a first away win and giving the fans a great afternoon out," added the Burnley boss, whose team are widely predicted to be in the relegation battle again this campaign.
"We're written off at the start of every season. It kills off a few things early doors and it allows the players that space for growth," added Dyche.
Chelsea were reduced to nine players in the 81st minute when Cesc Fabregas was shown a second yellow card but Dyche felt his team deserved the win.
"I thought we were strong early in the game, while it was 11 v 11. The sending-off made a difference and I thought we did really, really well to handle that and keep the ball and create chances," he said.
Wales striker Sam Vokes scored twice while Ireland fullback Stephen Ward hammered in a fierce drive.
“We scored three good goals and I think when you are talking about who you are playing against and where you are playing, that’s up there as one of the best 45 minutes of my time here," said the manager, who joined Burnley in 2012.
"It’s rare for any game in the Premier League to be three goals up at halftime, but particularly so when you are down at Chelsea.
"The shape and organisation was great. [Chelsea] had to respond, which they did, so credit to them, but we were disappointed with the two goals.
"Before that, we’d kept a good shape and I don't think they opened us up or made too many chances. But it's a big win.
"They're a fine side, even with 10 men."