Hazard completed the scoring three minutes from time with a composed finish from 12 yards as the Blues continued to improve under Jose Mourinho.
Here, Sports Mole analyses the game to see if Chelsea were deserving of the three points.
On target 5
On target 4
Was the result fair?
Schalke 04 enjoyed the better of the action before the break, but Chelsea took control in the second half to deservedly win this encounter. There appeared to be a lack of desire from the Chelsea attacking four to fight for the ball in the final third, but after a half-time ear-bashing from Mourinho, they worked relentlessly to ensure that their side comfortably secured the three points.
Schalke 04's performance
The German outfit looked two completely different teams either side of the break. During the first half, they allowed Chelsea little time on the ball while creating several opportunities, but they displayed little quality during a second-half showing that offered minimal joy to their passionate supporters.
Mourinho would have been furious with the majority of his team for their performance in the first half, but he would have been equally delighted with how they acquitted themselves after half time. Once in their stride, Chelsea looked a class above their opponents, and they will be confident of beating Schalke in the return match in 15 days' time.
Sports Mole's man of the match
Fernando Torres: Torres was hardly on course to win this award after his first-half display, but the Spaniard was like a man possessed during the second 45 minutes. He doubled his team's advantage, while showing a work-rate that inspired his teammates to follow suit.
This was a match that included no gaffes, but Schalke's defending was a bit shambolic for the second and third goals. They were chasing an equaliser, but the last man was left in three-on-one and two-on-one situations respectively, and Chelsea took full advantage.
Viktor Kassai made a couple of errors during the opening 20 minutes when he failed to halt play for a couple of Chelsea fouls, but all-in-all, this was a solid performance from the Hungarian, who officiated the Champions League final in 2011.
Schalke 04: Schalke must pick themselves up for their huge domestic clash with Borussia Dortmund at the weekend. They are already nine points behind their league rivals, and defeat could already spell the end of any realistic title challenge.
Chelsea: Chelsea host Manchester City on Sunday in what is expected to be a colossal tussle between the two Premier League title favourites. Two days later, the Blues will turn their attentions to the Capital One Cup, where they travel to Arsenal.