Eden Hazard blasted a penalty over the bar early on against the Israeli side.
The goal came soon after when Willian’s 35-yard free-kick evaded a crowd of players to bounce into the net.
Oscar doubled the lead from the spot, after Diego Costa was fouled, before the latter volleyed home and then Cesc Fabregas tapped in.
Chelsea went into the match under real pressure after making their worst league start to a season since 1986, with only one win.
In 2007, a slow start to the season followed by 1-1 draw at home to Norwegian side Rosenborg in the Champions League led to Jose Mourinho’s exit, and the Blues were desperate to avoid a similar European upset.
The pressure only increased when Hazard missed from the spot but, with the fans audibly behind manager Mourinho, the Blues never looked in danger of being upset by Israel’s champions.
While Manchester City, Manchester United and Arsenal lost their openers, Mourinho – who has won the competition twice – made light of all the pre-match crisis talk as Chelsea cruised to victory, despite fielding an experimental side.
Seeing John Terry, Nemanja Matic, Diego Costa and Branislav Ivanovic on the bench suggested Mourinho has had enough with his side’s dismal start to the season.
Some may point to having Saturday’s visit of Arsenal to think about, but leaving out his tried and trusted was a big call and a big message to his squad.
Willian was one player who took his opportunity with a very lively first quarter of the match on the right flank, before limping off with a hamstring injury, while 19-year-old midfielder Ruben Loftus-Cheek looked assured.
Ghana’s Baba Rahman made his debut at right-back but it was difficult to judge anyone defensively against a poor Maccabi Tel Aviv.
Costa emerged from the bench to earn Chelsea a penalty for their second goal. He then scored his first in the Champions League for the Blues with a volley from Fabregas’s cross.
The Spain international has endured a tough start to the campaign, with one goal compared to seven at this stage last time round, but looked more like his old self on Wednesday.
Hazard, on the other hand, again struggled to repeat the form that saw him named the PFA player of the year last season, although Chelsea did not need any of his magic against their very weak visitors. -BBC