The Spain striker bundled the ball into the visiting net on his competitive home debut on 63 minutes to give Jose Mourinho's side the lead before a deflected Eden Hazard shot 14 minutes later completed a merited win for Chelsea.
Nigel Pearson's newly-promoted Leicester side will rue missing three decent chances to snatch the lead with home goalkeeper Thibaut Courtois making one superb stop from David Nugent when he appeared certain to score.
The second half was a breathless affair after a forgettable first period, but Chelsea came on strong and could have ran out more comfortable winners despite needing some good fortune on both of their goals.
All the was missing was a goal for returning hero Didier Drogba, who thrilled the London's club's Russian owner Roman Abravomich when he emerged to replace Costa with 10 minutes remaining.
Chelsea have now picked up back-to-back opening wins with this accompanying the 3-1 win at Burnley on Monday. Leicester have one point from their first two matches in the Premier League.
37' - CHANCE! Costa sees a shot deflect off Moore before flying over after being played in by Hazard. Better from Chelsea. Leicester almost cut wide open.
48' - CHANCE! Oscar sees a shot come back off the post with Schmeichel beaten. Fine effort, but Leicester survive
49' - CHANCE! Schmeichel with a superb diving stop to deny Ivanovic's header. Wonderful save from the Leicester goalkeeper moments after Costa had appealed for a penalty.
55' - CHANCE! Mahrez slides in Nugent. In the clear, but Courtois somehow gets a touch to divert it wide. Brilliant stop.
57' - CHANCE! This game has suddenly come to life. Ivanovic picks out Fabergas, but his chipped attempt is clawed over by Schmeichel.
63' - GOAL! Costa slides the ball into the net. Chelsea lead 1-0. Oscar's pass to Ivanovic. Bit of a scramble, but Costa reacts quickest. Home side move ahead.
77' - GOAL! Hazard with the second goal for the home side. Under De Laet, and then under the body of Kasper Schmeichel. 2-0, and it is game over.
88' - CHANCE! Willian forces Schmeichel to make a decent stop. Almost time up. Leicester will be happy to see the back of this match.
Chelsea - Leicester
Chelsea have won their opening two matches for the fifth time in six seasons under Jose Mourinho.
Chelsea have won their opening two matches for the seventh time in the last eight Premier League seasons.
Chelsea extend their unbeaten run to five in the Premier League and continue their record against promoted sides in the English top flight, having now got 304 points in 132 matches. Chelsea have now won seven matches in a row against Leicester, in all competitions.
Why was Roman Abramovich looking so happy? The Chelsea owner looked delirious at points. Either he was sniffing some Russian vodka during the match, or else he was marvelling at the fresh style of Chelsea. With Cesc Fabregas added to the mix, Chelsea are moving the ball very well. And in £32m man Diego Costa, they have a forward to finish. Fair enough the first half was not great, but the second period was highly enjoyable fare. And Didier Drogba emerging from the technical area just completed a fine afternoon's work for the home side.
MAN OF THE MATCH
Thibaut Courtois (Chelsea) - Managers stand or fall on such key decisions, and Jose Mourinho's call to replace the unfortunate Petr Cech already looks to be the right one. The Belgian goalkeeper was a key figure in ensuring Leicester did not strike first. You just wonder whether or not Cech will be content to sit looking on for too much longer.
Chelsea: Courtois 8; Ivanovic 7, Cahill 7, Terry 7, Azpilicueta 7; Matic 7, Fabregas 7, Schurrle 6, Oscar 7, Hazard 7, D Costa 6..subs: Ramires 6, Willian 6, Drogba 6
Leicester: Schmeichel 7, De Laet 6, Morgan 7, Moore 7, Konchesky 6, Mahrez 7, King 6, Hammond 6, Schlupp 6, Ulloa 6, Nugent 5..subs: Albrighton 6, Taylor-Fletcher 6, Wood 6
THE MATCH IN A TWEET
- Sports & Recreation
- Diego Costa
- Jose Mourinho
- Thibaut Courtois
- Didier Drogba
- Leicester City
- Premier League
- Eden Hazard