Just nine months on from winning the Champions League, the west Londoners only just managed to overcome the side third in the Czech top flight at Stamford Bridge.
Skipper John Terry admitted Chelsea put in a disappointing performance before Hazard’s late strike.
Holding a 1-0 advantage from the first leg in the Czech Republic, Chelsea were strong favourites to advance but David Lafata’s 17th-minute strike changed the complexion of the match.
Chelsea poured forward but allowed Sparta to create chances on the counter-attack before Hazard’s late goal levelled it on the night to spare Chelsea’s blushes.
“It was disappointing, the way we started, but we’re delighted to go through,” Terry said. “We left it as late as we could as sometimes that’s the best way. It wasn’t our best performance but we’re in the next round and we’re happy with that.”
However, Terry believes Chelsea showed good spirit to keep fighting and deserved their reward.
“We’ve kept going and going and going,” he said. “The first 80 minutes, nothing went for us. We had a lot of attempts on goal but it didn’t go for us. But the persistence from the lads was fantastic.
“We’re still very disappointed to be out of the Champions League and watching that on Tuesday and Wednesday nights is frustrating but this is a good competition and we’re in it to win it.”
With Manchester City looming on the horizon this weekend in the Premier League, Chelsea upped the ante in the closing 15 minutes in a bid to avoid extra-time.
However, Vaclav Kadlec twice came close in stoppage time, before the travelling fans’ hearts were broken.
Hazard was the man who did the damage, finding space in the left-hand side of the box to fire home.
CHELSEA: Cech, Azpilicueta, Terry, Cahill, Bertrand, Ramires, Mikel, Moses, Mata, Torres, Oscar (Hazard 67).
SPARTA PRAGUE: Vaclik, Zapotocny, Holek, Svejdik, Hybs, Prikryl, Vacha, Krejci, Matejovsky, Lafata (Kweuke 82), Kadlec (Bednar 90).
Ref: A Stavrev (FYR Macedonia).