Karim Benzema’s peerless exhibition of clinical marksmanship rescued the draw for a Real side muddled by a change of formation and the Blues’ technical and tactical acumen.
Hazard – who has been beset by injury problems since swapping Chelsea for Madrid in a huge transfer back in 2019 – came off the bench just after the hour-mark at Estadio Alfredo Di Stefano, but could not find a winner for Real.
The result means Real will need to score in west London in the return leg to stand any chance of reaching a final against either Manchester City or Paris Saint-Germain.
Real are also fighting for domestic glory, with Zidane’s men two points off LaLiga leaders Atletico Madrid.
Following the draw with Chelsea, Hazard told BT Sport: “We have to go there to try to win the game.
“It’s always good to play against friends – I have a couple over there – but now I’m a Real Madrid player, I just want to win.
“It doesn’t matter if it’s against Chelsea or another team.”
Real struggled with a three-man defence in the opening exchanges, and were fortunate to not be out of the game – and the tie itself – before Benzema levelled.
Los Blancos tightened up in defence and midfield in the second half, and Hazard added: “The manager decides what formation we play, we know how to play with three at the back but we can also play with four.”
Additional reporting by PA.