Only time will tell if the imposing Englishman's heroics will see him play more minutes in the Premier League, but he will surely be given a regular stating berth during Chelsea's Europa League campaign.
A second-half header from Olivier Giroud - his first goal of the season - proved to be the difference between the sides, although BATE struck the woodwork on three occasions.
BATE manager Alyaksey Baha on Chelsea test: "We have followed all the games Chelsea have played. But I don't want him to be anxious about scoring because for us he's very important".
'But I don't want him to be anxious about scoring because, for us, he's very important and very useful. "I was lucky, I think".
The Stamford Bridge outfit also remain the only unbeaten side in Europe's top five leagues in all competitions following their win on Thursday evening.
With that in mind, it could be argued that it would have been good to have played Hazard anyway, but he will feature for other reasons rather than that, as the Italian confirmed when he faced the press.
"We analyse the games (against Arsenal) so we learnt from our mistakes". There was all the conditions to play very badly, for the cold, for the opponents, for the pitch, for everything.
"It was better in the first 20 or 25 minutes of the second half". I think it is better for him to stay fit with two or three trainings than only with matches.
The visitors quickly started to monopolise possession, but despite seeing over 70 percent of the ball in the first half, they failed to even manage a shot on target against a well-drilled BATE outfit.