The Blues impressed despite falling behind to a fabulous header from highly rated Eintracht forward Luka Jovic, making most of the running after Pedro fired home an equaliser shortly before half-time.
Hazard came on after the hour as Chelsea sought to drive home its control of the contest and it is in a prosperous position for next week's return at Stamford Bridge.
After the match, Sarri explained concerns over the Belgium star's heavy workload for club and country was behind the decision.
"Eden was on the bench because, in the last period, he played 10 matches in a row," he said.
"It's impossible to play that many. For us, this was match number 59 I think, and Hazard also played eight matches in the national team.
"For a player, it's impossible to play 70-75 matches in a season. And so, sometimes, Hazard like all the other players needs to rest. Or not to rest, but not to play for 90 minutes."
Despite keeping his star man in reserve, Sarri did not change from his usual pre-match routine when it came to announcing his line-up.
"[I told him] in the meeting before the match. Like all the others," he said.
"Usually, I don't speak with the players that I want to put on the bench. Eden, for me, is a player. Probably he is the best player, but he is a player.
"And so I have to do it this way. Otherwise I have to speak to everyone for every match and I don't have the time."
Chelsea did not suffer the drop-off in performance they often have without Hazard this term, thanks in large part to a superb all-action midfield display from Ruben Loftus-Cheek.
The England international created Pedro's leveller and twice went close to scoring after the break.
Cramp ended his outing during the latter stages but Sarri talked up the benefit of the 23-year-old being free temporarily of his persistent back pain.
"Loftus is a very important player. He improved a lot during the season," he said.
"When he is at the top physically, he's a very important player. He's always in trouble with his back and it's not easy for him to have training with consistency.
"But in this match he was really fit. He played a very good match."
Sarri remains in pursuit of his first major honour as a coach and suggested there is a sense of unfinished business for him this season, having seen Chelsea fall agonisingly short in a Carabao Cup final penalty shoot-out against Manchester City in February.
"I don't want to play the final; I want to win it," he added.
"Three months ago, we were in trouble in a very difficult championship and it's not easy to react, but we were able to react.
"Now, in the last 15 days of the season, we are fighting for the top four [in the Premier League] and the final in the Europa League, so we deserve a trophy."