John Terry and a Kyle Walker own-goal helped Chelsea claim the 2015 League Cup in an all-Capital Wembley final on Sunday.
Chelsea put up a commanding display with captain Terry opening scores with their first shot on target after Christian Eriksen had hit the woodwork for Spurs.
Costa teed up with fellow Spaniard Cesc Fabregas to double the Blues’ lead in the 56th minute, when his shot took a huge deflection off defender Kyle Wallker into the net.
Just like in his initial spell in 2004, the Capital One Cup is Chelsea’s first trophy since Jose Mourinho’s return and the Portuguese’s first since 2012.
The final whistle was met with a rapturous applause from the 89,297 crowd gathered at the Wembley Stadium, before Terry, who was voted Man of the Match, led his team-mate up the terrace to collect the prestigious Alan Hardaker trophy.
Chelsea are now tied on five League Cup triumphs with Aston Villa in third and trail leaders Liverpool by three.
The last final involving both London neighbours ended in disappointment for the then Avram Grant Chelsea seven years ago but, with either team tied on four successes prior to kick-off, the westerners were clear in their intention to pull ahead on the roll of Cup honours.
Mauricio Pochettino’s men never really troubled Chelsea, aside Eriksen’s tenth-minute free-kick which came off the crossbar to safety.
And without the suspended Nemaja Matic and the injured John Mikel Obi, Mourinho’s preference for a central defender Kurt Zouma in a defensive midfield role proved effective for the Stamford Bridge outfit.
Spurs’ other attempt in the opening period was comfortably dealt with by Petr Cech- preferred instead of Thibaut Courtois- after England Under-21 Harry Kane ended a fine run with a low shot from 20 yards.
Chelsea capitalised on their opponents’ defensive mix-up to claim the lead right at the break. Willian’s free-kick from the right was deflected off Dany Rose’s head to the feet of Terry, whose shot took a second deflection off Kane past Hugo Loris into the net.
Another deflection resulted to Chelsea’s second goal 11 minutes after the break, as Fabregas released Costa in on goal inside the Whites’ penalty area only for the Spanish striker’s seemingly harmless shot across goal to be deflected past Lloris inside the near post by Walker.
There was barely any other salient effort from both sides before referee Anthony Taylor blew the final whistle.
Mourinho has now won his first trophy since lifting the Spanish La Liga with Real Madrid in 2012 and Chelsea their first since the Europa League final triumph over Benfica in Amsterdam in 2013.