The hosts were given hope of a huge upset when Scott Arfield put Burnley in front in the 14th minute, but it was all Chelsea after that. Costa showed why Chelsea spent $53 million to bring him in from Atletico Madrid when he scored the tying goal just three minutes later, and Fabregas set up Andre Schuerrle with a sublime pass in the 21st as the German World Cup winner made it 2-1.
Fabregas then sent in a corner in the 34th that Branislav Ivanovic volleyed into the net.
Costa and Fabregas were the two major offseason recruits for Jose Mourinho's team, and they showed right away why their arrivals have made Chelsea the bookmakers' favorite for the title.
Fabregas, especially, was involved in nearly every Chelsea attack on his return to the Premier League - and may have given Arsenal manager Arsene Wenger second thoughts about his decision not to re-sign his former captain from Barcelona this summer.
''He really was the maestro, he controlled the tempo of the game,'' Mourinho said. ''He was the man that dictated the speed, the intensity and the direction of the game.''
FRANKFURT, Germany (AP) - Schalke was stunned 2-1 by third-division Dynamo Dresden in the first round of the German Cup.
Hamburger SV squeezed into the second round when goalkeeper Rene Adler saved two penalties in a shootout win over third-division Energie Cottbus.
Hamburg rallied to tie the game 1-1 in regulation and went ahead in extra time, only to see Cottbus level late for 2-2.
Schalke, which will play in the Champions League this season, became the fifth Bundesliga team to be knocked out in the first round, following weekend losses by Mainz, Stuttgart, Augsburg and Paderborn, while Dresden celebrated its return to the cup competition with a huge upset. Dresden was excluded from last season's tournament because of fan trouble.
BARCELONA, Spain (AP) - Neymar and Luis Suarez played for the first time since their dramatic World Cup exits, with the Brazilian star scoring twice Monday in Barcelona's 6-0 rout of Mexican champion Leon in a preseason tuneup.
The last time Suarez played he infamously bit an Italian opponent at the World Cup, drawing a four-month ban from competitive matches.
The Uruguayan striker has since transferred to Barcelona from Liverpool. He was cheered by his new fans at Camp Nou during the team's introduction. He entered as a substitute in the 75th minute to more applause.
Neymar hadn't played since fracturing a vertebra during the World Cup on July 4, ruling him out of the rest of the tournament. He was deemed fit to play hours before the game against Leon.