Costa scores again as Chelsea snare Foxes
Chelsea's Brazilian-born Spanish striker Diego Costa celebrates scoring the opening goal during the English Premier League football match between Chelsea and Leicester City at Stamford Bridge in London on August 23, 2014 - by Ian Kington
After a goalless first half, Chelsea twice almost took the lead at the start of the second period.
Oscar hit the far post with a curling shot from the right before Branislav Ivanovic's header was well saved by Kasper Schmeichel, son of former Manchester United goalkeeper Peter.
Leicester, who held Everton to a 2-2 draw last week, then had a chance of their own when David Nugent burst clear only for the Foxes striker to be denied by Thibault Courtois, again preferred by Jose Mourinho to Petr Cech, when one-on-one with the keeper.
But £32 million ($55 million, 40 million euros) Spain striker Costa, who scored in last week's 3-1 win at Burnley, marked his home debut by turning in Ivanovic's cross from eight yards out in the 63rd minute.
Chelsea then doubled their lead at Stamford Bridge when Eden Hazard's 77th-minute shot beat Schmeichel after deflecting off Leicester defender Wes Morgan.
"We didn't play good in the first half," Chelsea manager Mourinho told Sky Sports.
"Leicester came with great defensive intensity, trying to scare us in counter-attack and we were a bit slow - slow in moving the ball and slow thinking and we needed to change and we did that," the Portuguese added.
"I don't forget they had a good chance with the result 0-0 but we had so many chances, so many opportunities to score obviously we deserved the victory."
Leicester boss Nigel Pearson was left to rue Nugent's squandered opportunity.
"We're disappointed...I thought we played exceptionally well in the first half but it's about taking your chances when you get them," he said.
Swansea, fresh from their shock opening day victory away to Manchester United, also made it two wins from two with a 1-0 success at home to Burnley secured by winger Nathan Dyer's 23rd-minute goal.
"I knew it would be a tough game," Swansea manager Garry Monk told the BBC. "But you have to applaud our players."
Burnley boss Sean Dyche added: "It's disappointing that we didn't come away with anything, but you could see the growth from us."
West Ham bounced back from a 1-0 defeat by Tottenham Hotspur with a 3-1 win away to managerless Crystal Palace.
The Eagles, without a manager after Tony Pulis quit before the season started in a row over transfer funds, had seen sporting director Iain Moody resign in midweek following the fall-out from the publication of offensive text messages he had shared with Malky Mackay while the pair were at Cardiff.
- Hammers' quickfire double -
Any hope of better news on the pitch was shattered when Palace conceded two goals in three first-half minutes.
Argentinian striker Mauro Zarate marked his Hammers debut with an impressive 34th-minute volley before England winger Stewart Downing added an equally stylish second, cutting in from the right flank before curling in a 20-yard left-foot shot.
Palace pulled a goal back in the 48th minute through Marouane Chamakh.
However, the Hammers made it 3-1 in the 62nd minute when striker Carlton Cole scored his first goal since February when he volleyed home from inside the penalty area.
Southampton and West Bromwich Albion shared the points in a goalless draw and Saturday's early kick-off between Aston Villa and Newcastle ended the same way.
Newcastle, beaten 2-0 by reigning champions Manchester City last weekend, have still to score in the Premier League this season after centre-back Mike Williamson was sent off in stoppage-time for a second bookable offence.
Arsenal are away to Everton in Saturday's late kick-off.
Louis van Gaal will go in search of his first competitive win as Manchester United manager at north-east side Sunderland on Sunday.
Meanwhile former Spurs boss Harry Redknapp will return to White Hart Lane as manager of London rivals Queens Park Rangers.
Sunday's other Premier League fixture sees Hull, 1-0 winners over QPR last weekend, at home to Stoke.
The second round of Premier League matches is completed by Monday's clash between Manchester City and Liverpool, last season's runners-up, at Eastlands.
By then former City striker Mario Balotelli could be a Liverpool player if his proposed £16 million ($27 million, 20 million euros) transfer from AC Milan has been completed, although any deal will come too late for him to be registered to play on Monday.