Marcos Alonso gave Chelsea a 13th-minute lead, heading home the rebound when Diego Costa's header looped up off the crossbar.
The wing-back's robust challenge on Hector Bellerin that allowed him to score is likely to draw post-match rancour from Arsene Wenger, but the suspended Gunners manager could have no complaints when those alongside him in the stand were brought to their feet in the 53rd minute.
Hazard made his mazy way from his own half to the edge of the Arsenal six-yard box to score the kind of goal that can come to define title triumphs.
Arsenal could muster little in the way of a response as they limply succumbed to a defeat more chastening than the one they dealt out to Antonio Conte's men in September, when the prospect of Wenger besting an elite opponent in the dugout briefly re-emerged.
At Stamford Bridge, as substitute Cesc Fabregas collected Petr Cech's woeful clearance and lobbed into an unguarded net, it was nowhere to be seen.
By the time Olivier Giroud headed a stoppage-time consolation from Nacho Monreal's centre, the fact Liverpool can shave Chelsea's advantage to 10 points by beating Hull City later on Saturday felt of greater significance.
Chelsea's measured playing out from the back has been a feature of their transformation under Conte but goalkeeper Thibaut Courtois and David Luiz passed their way into trouble in the second minute.
Mesut Ozil intercepted and Alex Iwobi's low drive deflected agonisingly wide with Courtois beaten.
The hosts' first opening came from a set-piece when Alex Oxlade-Chamberlain brought down Victor Moses and Gary Cahill headed into the turf and over.
Arsenal failed once more to deal with their opponents’ aerial threat when they fell behind.
Costa planted a header from Pedro's excellent right-wing cross against the crossbar and, with Cech peeling himself off the turf, an onrushing Alonso emphatically beat the stationary Bellerin to the rebound.
The groggy Spain right-back was substituted shortly afterwards after failing to recover and Costa fired into the side netting as Chelsea scented blood.
Shkodran Mustafi was redeployed to right-back and earned a booking for clattering Hazard, although the Belgium playmaker recovered sufficiently to orchestrate a flowing 32nd-minute move that ended with Cech unconvincingly spilling Pedro's attempt behind.
Bellerin's replacement Gabriel had a glorious chance to equalise before the break but could not keep his free header down and Courtois acrobatically clawed to safety.
Early in the second period, Laurent Koscielny made a vital challenge on Hazard as the last man but, shortly afterwards, the mercurial Belgian effortlessly shimmied past the France centre-back - having unceremoniously shrugged off Francis Coquelin – to score a stunning solo goal.
Wenger shuffled his pack to little effect – as if rearranging the deck chairs on a once-famous ocean liner – and an increasingly understaffed midfield appeared ever more to Hazard's liking.
His old protege Fabregas applied the final insult in the 85th minute and declined to celebrate. The midfielder was in a small majority as Stamford Bridge lapped up a famous triumph – Giroud offering the briefest punctuation to the party atmosphere.