Mourinho's side went into their Group G opener in turmoil after Saturday's dismal 3-1 defeat at Everton left them with only one win from their first five Premier League matches.
That miserable sequence was Chelsea's worst start to a season since 1988 and it provoked a barrage of criticism for Mourinho and his under-performing English champions.
But Mourinho promised changes after the Everton loss and the Blues boss was true to his word as he axed John Terry, Diego Costa, Pedro Rodriguez, John Obi Mikel, Nemanja Matic and Branislav Ivanovic.
But lacklustre Maccabi were the perfect opponents for Chelsea to rediscover a semblance of their form and Willian opened the scoring before Oscar showed Hazard how to do it by converting a penalty on the stroke of half-time.
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Costa came on to net in the second half and Cesc Fabregas added gloss to the scoreline with a late tap-in.
It was far from a vintage Chelsea performance, but Mourinho will hope it provides a foundation for future success, starting with a sterner test against Arsenal in the Premier League this weekend.
Remy's defence-splitting pass put Willian through on goal and the Brazilian winger was sent crashing to the turf by Maccabi goalkeeper Predrag Rajkovic.
However, Mourinho still felt hard done by when German referee Felix Zwayer decided not to send off Rajkovic and he screamed in anger on the touchline when he saw the yellow card.
There was even worse to come as Belgium midfielder Hazard, showing a lack of composure that encapsulated his current struggles, blazed the penalty high over the crossbar.