Blues open Champions League campaign with 4-0 home victory
Willian, Oscar, with a penalty, Costa - on as a substitute after being omitted as one of six changes following the loss at Everton - and Cesc Fabregas scored as the Blues opened Group G with a 4-0 victory.
It was their first home win of the season and second in all after a miserable start to the campaign which has sparked suggestions of a crisis.
Chelsea may be floundering domestically, but once again they lead the way for English clubs in Europe after Arsenal followed Manchester United and City in making a losing start.
Sterner tests await Jose Mourinho's side - first up the Gunners here on Saturday - but there were signs of improvement against albeit limited opposition.
Problems remain and Eden Hazard, in particular, still appears short of his effervescent best, blazing a sixth-minute penalty over, but Ruben Loftus-Cheek was among those who impressed after recovering from a yellow card in the opening minute.
Mourinho said he knew what the consequences of changes would be - speculation of strained relationships - but that he was planning alterations anyway against a side in the group stages for the first time in 11 years.
Captain John Terry, Branislav Ivanovic, Nemanja Matic and Costa were omitted, with Baba Rahman among those drafted in, making his debut at left-back.
Maccabi Tel Aviv advanced by beating Basle in the play-offs, but never looked like emulating the Swiss side, who beat Chelsea home and away two years ago.
The Israeli team are managed by former Chelsea midfielder Slavisa Jokanovic, who last season led Watford to the Premier League and a 3-0 FA Cup third-round loss at Stamford Bridge.
Jokanovic was hoping for a tighter contest, but there were gaping holes in his side's defence from the start.
Mourinho was infuriated Predrag Rajkovic was not sent off for bringing down Willian for the first spot-kick, but luck was on the Blues' side as the Brazilian curled in a free-kick which evaded everyone.
He later went off with a hamstring problem, with Costa coming on.
Goalkeeper Rajkovic might have conceded another penalty when Loftus-Cheek was brought down two minutes before the interval.
Then the visitors' two Tal Ben Haims failed to get a grip of Costa, who was felled by the former Chelsea defender, with Oscar converting from the spot.
Costa, who failed to net in Europe for the Blues last term, emphatically volleyed in a cross from Fabregas - a combination which worked wonders for Chelsea in the first half of last season but has stuttered since - before the Spain playmaker struck the fourth on the counter-attack.
Hazard burst down the centre, played it right for Loic Remy, whose shot was palmed by Rajkovic into the path of Fabregas to score.
There were still signs of weakness which the visitors failed to exploit.
Eran Zahavi missed a free header and Nosakhare Igiebor somehow failed to convert after 88 minutes as Chelsea kept a clean sheet for the first time this season.