Hazard is the Blues' regular penalty taker but he allowed Drogba to net from the spot in a 6-0 rout of Maribor in a Uefa Champions League Group G tie.
Drogba reunited with the Premier League leaders in the summer, having previously left the Londoners on a high after slotting the deciding penalty in the 2012 Champions League Final win over Bayern Munich.
"To finish with a penalty and start again with another penalty is nice," Drogba, who ended a seven-game scoring drought, told ITV.
"I was very lucky with the way we played. We scored two early goals but we didn't stop, we continued to play and that's the result."
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The Ivorian added: "I wanted to score that goal so I asked him and he said yes.
"This is the spirit we have in this team. We share goals and are happy when everyone is scoring. I think they are also happy for my confidence."
However, Chelsea boss Jose Mourinho was less than impressed with Hazard's generosity.
"I wasn't particularly pleased because I have my choices and Eden is the first choice," said the Portuguese.
"Drogba, Oscar, Fabregas and Diego Costa are there in case Eden is off the pitch."