Clarets boss Sean Dyche hailed a "professional performance" after following up the win at Blackburn with a home victory over Huddersfield Town.
The Terriers made Burnley sweat in the closing minutes after a Michael Duff own goal halved the deficit following two first half Andre Gray strikes.
But Dyche felt his side had done enough ahead of that late scare to win more convincingly.
He said: "I think we did (made hard work of it), but you have to remember there are two teams out there, battling and fighting, for different reasons, to win a game.
"I thought we controlled a lot of the game, they had some good possession but never really opened us up, and we're used to that from the Premier League where teams have more possession, and it's about being ready to control the game when you have the ball, which I thought we did well.
"We scored two very good goals. The first was on the back of an 11-pass move, from our keeper, through the midfield, into the forwards, and allowing Andre to get in behind for a penalty.
"Thank goodness we finally got one...
"The second was very similar, good movement, a good passage of play, some fine link up play between Vokesy and Andre, for a superb strike.
"The last five or six minutes makes a game of it, with them scoring from a corner where we should have gone 3-0 up, but in the end, it would have been a travesty if we didn't win that game."
And he feels his side are starting to find more fluidity to their play: "I thought we created some good chances, I was really pleased with the chances and how they came about, some fluid play, from directness, from playing out wide, good crossing, and a set piece with the penalty, so there were good signs overall.
"I spoke about trying to find that connection on the pitch between the players, because it is a relatively new group, and there are signs of it.
"Good play has to end with a chance, and that was on show.
"I'm always demanding of the group, and I said afterwards there are still some details we need to work on, but I believe in the strong mentality we have here, as a club, and after a big result last weekend, probably a few people are waiting - 'is it after the Lord Mayor's Show?', and I thought we gave a very professional performance in order to win."
Gray has six goals in nine starts now, and eight in total for the season, and Dyche added: "Two goals again, he's enjoying it here, he's enjoying the group he's playing with, and he's producing the goods.
"Some of his link play with Vokesy was excellent at times, and I still think there's more to come.
"The players on the bench can affect the game as well, and probably would have today if we had got the third goal. We were comfortable but a third goal really kills it.
"But all credit to Huddersfield, they kept going to try and get something from the game, and that is the Championship, people don't down tools, not that they do at any level, but certainly not this.
"We had to deal with that, and overall we did."