Jose Mourinho has already admitted that the Blues will be ‘contenders’ this season, but his side made a slow start as Scott Arfield fired the newly-promoted hosts into a shock 14th-minute lead.
Chelsea wasted little time in responding, though, as debutant Diego Costa fired home an equaliser three minutes later before a stunning passing move culminated in Cesc Fabregas picking out Andre Schurrle to slot the visitors ahead.
Branislav Ivanovic then converted a Fabregas corner to all-but wrap things up after 34 minutes as Chelsea topped the Premier League table with what proved to be a relatively routine win.
Fabregas was named Man of the Match on his first appearance in a Chelsea shirt while Costa also caught the eye, and Terry is hopeful the new arrivals will boost their chances of a first title since 2010.
Terry told Sky Sports: "We’ve made some very big signings. Diego’s come in and held it up well tonight and got on the scoresheet which is a great start for him as well.
"We’ve made some good signings and we’re hoping to win the league. That’s our target this year.
"This is going to be very tough this season, we’ve seen at the weekend the quality of the teams but we’ve picked up three points tonight and we move onto the next."
Terry also hailed his side’s display at Turf Moor as they rose above the occasion and conditions to see off Sean Dyche’s men.
"We knew it was going to be very difficult here tonight at Burnley but I thought the football we played, some of the movement and the play for the goals was a different class," he said.
"Cesc’s is probably the pick of the bunch for Schurrle. It was a tough game tonight but we saw it out in the second half.
Asked about Mourinho's tactics, Terry added: "He wants us to play from the back, he wants us to get the ball and move it.
"I think we dropped too many points away from home last year to the lesser sides. We had to come here and fight and want it more than them. I think we had that.
"But more in abundance we had plenty of possession and quality play."
Fabregas, who joined from Barcelona for a reported £30million fee this summer, walked away with the Man of the Match champagne at full-time having played a hand in all three Chelsea goals, including a sublime pass for the second.
The Spaniard said: "You always want to do well. I love playing football and I think we have a talented young team.
"So far, so good. I’m enjoying it. Everyone has treated me very well so I’m happy.
"They made it so easy for me. Everyone has welcomed me since day one. I’m very comfortable with all the staff and all the players.
"We have a very good connection so I’m expecting a really good year in front of them.
"It’s something that I probably would have never expected but football is unexpected – it brought me here and I will give it my best.
"I’m very happy with the moment."