Rafael Benitez's side went into the match boasting a 1-0 advantage from last week's first leg in the Czech Republic, leading the Spaniard to rest Frank Lampard and Branislav Ivanovic ahead of Sunday's trip to Manchester City.
But Sparta took a shock lead - and levelled the tie - on 17 minutes when David Lafata slotted home after Vaclav Kadlec pulled back Marek Matejovsky's quick free-kick.
Misfiring striker Fernando Torres wasted a whole host of first half chances for the Blues, including heading over from 12 yards just before the break after getting between defenders to meet John Obi Mikel's cross.
Soon after the break, Oscar made a great run at the Sparta box before teeing up Ramires, who hit the post with a deflected effort.
Torres was played in one-on-one by Ramires soon afterwards and he tried to lob the on-rushing Tomas Vaclik but the keeper saved.
Chelsea skipper John Terry, who returned to the side after being absent for the first leg, volleyed at goal from 12 yards but Vaclik palmed away.
At the other end, Matejovsky made a strong run before shooting from 25 yards out in the centre but his low effort went just wide of Petr Cech's post.
Mikel then floated a long ball forward to Torres who chested it down to Victor Moses, with the winger letting one fly from 22 yards but Vaclik parried out for a corner, which Sparta subsequently cleared.
Ramires created a yard of space for himself to the right side of the box but pulled his shot wide before Tomas Zapotocny blasted just over from outside the box.
The clash looked to be heading into extra-time before Hazard scored a great individual goal in stoppage time with virtually the last kick of the game to spare the Blues' blushes.
Chelsea will now face Steaua Bucharest in the next round after but this display was far from convincing from the reigning European champions.