The second-half substitute secures his side's progression to the Europa League last-16 stage with last-gasp stunner on another frustrating night at Stamford Bridge
The European champions were seconds away from being taken into extra-time after David Lafata’s strike levelled the aggregate score following Chelsea’s 1-0 win in the first leg in Prague.
But Hazard struck a sensational left-footed shot into the roof of the net with virtually the last kick of the game to set up a clash with Steaua Bucharest in the next round.
Hazard’s strike saved Chelsea’s blushes after a frustrating evening that saw manager Rafa Benitez booed for his substitutions while the name of former manager Jose Mourinho was sung loud and clear in west London.
It was also a miserable night for striker Fernando Torres, who missed a number of clear-cut chances and himself felt the anger of the Blues faithful.
Chelsea made four changes that won the first leg as John Terry returned to the heart of the defence while Frank Lampard and Branislav Ivanovic were rested ahead of this weekend’s trip to Manchester City.
Benitez admitted before the game that he had half-an-eye on the City clash and his players seemed to take their eyes off the ball completely during an insipid opening period in which the visitors controlled large spells of the match.
It was also marked by some woeful finishing by £50 million striker Torres, who could have given Chelsea the lead in the fourth minute but swept his right-footed shot wide from 12 yards after Victor Moses’ pass.
In the 11th minute, Torres again missed a glorious chance to put the Blues ahead on the night as he volleyed Juan Mata’s cross over the bar, opening the door for Sparta Prague to take advantage of the hosts’ wastefulness.
That happened in the 17th minute. From a quick free kick, Vaclav Kadlec worked space in the box and squared for Lafata to place his shot into the roof of the net from 10 yards out to level the tie.
The goal silenced the already quiet Stamford Bridge crowd and the Chelsea supporters’ frustration grew as Benitez’s men continued to squander chances.
Mata forced Sparta Prague goalkeeper Tomas Vaclik into a fingertip save after brilliantly juggling the ball in the penalty area before Torres put a free header over the bar from seven yards.
Chelsea were booed off the pitch at the break and started the second half with greater attacking energy as Ramires’ shot was deflected onto the post after good work from Oscar.
Torres then missed yet another excellent opportunity, the striker’s clipped effort saved by Vaclik after he raced through on goal.
At the other end, Sparta Prague reminded the Premier League side of their threat on the counter-attack as Marek Matejovsky fired a low shot inches wide of the post from 20 yards with Petr Cech beaten.
Then, as the clock ticked past 90 minutes and the teams began to prepare for extra-time, Hazard smashed a wonderful left-footed shot high past Vaclic to the relief of Stamford Bridge.