Hazard's sublime first-half opener at Stamford Bridge - his seventh goal of the season - looked like giving the Blues another victory over Liverpool three days after the Belgian's Carabao Cup victor at Anfield.
Hazard and Sturridge were in fine form, and the Chelsea star approached his former teammate in the tunnel after the game.
"Virgil will try everything to be ready and I know how it sounds but, as long as you are not seriously injured, like [something] broken or ruptured, or have a proper strain, ..."
"I said to him the goal wasn't bad, to be fair".
England worldwide Sturridge, 29, has never been assured of a place in the Liverpool attack under Jurgen Klopp, while a succession of injuries have taken their toll. The former Chelsea forward's stay at Anfield looked to be over last season after a failed short-term loan spell at West Brom which saw him spend more time on the sidelines than on the pitch.
Liverpool’s Jurgen Klopp describes Chelsea’s Mateo Kovacic as Formula One auto
Maybe we won them previous year but it was almost always over the top what we have to do. And even then still not possible to score a goal, but he did because of a ideal finish.
"He's such a threat still and it's really good".
Klopp also attempted to downplay Mohamed Salah's withdrawal after 66 minutes, with Xherdan Shaqiri replacing the Egypt worldwide, who squandered a number of good opportunities during his return to Chelsea.
Although he was forced onto his weaker left foot Hazard still managed to drill the ball low past Alisson Becker for his seventh goal of the season.
"It was not Mo's best game of his career, 100 per cent", Klopp said.
"Me and "Studgey" are getting a bit older now", Liverpool midfielder James Milner said, referring to Sturridge.
"It's like riding a bike and it's not that you wake up in the morning and can not ride a bike anymore".
- This was the 38th home Premier League game that Hazard has scored in - he has never ended on the losing side in any of those games (W34 D4 L0).