Hazard played for 62 minutes as Chelsea advanced to the Europa League knockout stages with victory at BATE Borisov of Belarus, having made his return as a substitute in last Sunday's win over Crystal Palace.
Chelsea will be looking to keep the pressure on at the top of the table with a win when they welcome Everton to Stamford Bridge on Sunday afternoon.
"It's a nice thing to have, even the other day when it went 1-1 you were sitting there and you were like "at least Hazard has not still got to come on", do you know what I mean?" Barkley arrived at Chelsea carrying a hamstring injury and played just four times under Antonio Conte, who Sarri succeeded in July.
Eden Hazard may not play a full 90 minutes for Chelsea until after the global break against Tottenham.
However, the Blues were creating very little in the final third, with only a miscued Olivier Giroud volley from a floated Ross Barkley pass coming anywhere near to breaking the deadlock. "I had fever", Sarri said.
Chelsea went straight onto the front foot after the restart - presumably after some stern words from Sarri - and the visitors found the breakthrough in the 52nd minute as Giroud directed a glancing header inside the near post after meeting Emerson's cross from the left flank.
"For me, football is about levels and, if you don't defend properly and you don't do the basics well enough, high-level players and high-level teams normally punish you and that was the case tonight", Gerrard told the Rangers website. The form they (the new players) are in. It is normal to look around and think, 'With what club can I achieve that with?'
"On the day I might get a few nerves as it will feel a bit odd".
Cesc Fabregas is the only doubt after missing out with illness last night, but the Spaniard would be unlikely to start anyway.
Chelsea are nearly back to full strength after both Eden Hazard and Olivier Giroud got minutes under their belt in the Europa League.
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