Leaders Chelsea maintained their seven-point cushion over Tottenham in all the style befitting champions-elect and now need at the most 15 points from seven matches to seal the silverware.
Diego Costa's woeful fly-hack forced an own goal from Adam Smith to hand Chelsea the lead, before Hazard outfoxed Artur Boruc for his 14th Premier League goal of the season.
Joshua King's deflected strike handed Bournemouth hope of a recovery, but Marcos Alonso's curling free-kick sealed Chelsea's fifth win in six league matches.
Simon Johnson assesses the key talking points...
Moses shows what Chelsea have been missing
It's only been two games, but Chelsea fans were relieved to see the Nigeria international back in the first XI tonight.
Chelsea have not looked as balanced or as comfortable without Moses playing at right wing-back.
A combination of a toe and a calf injury had forced him to spend a bit of time on the sidelines.
It underlined once again what a dramatic change in fortunes Moses has experienced at Stamford Bridge that the team have missed him so badly.
At Bournemouth he showed why, especially in attack as he marauded down the right hand side time and time again.
It was his pass that set up Chelsea's opening goal and he could have got on the scoresheet a couple of times himself.
Arsenal must secure Wilshere on a new contract
It is still remarkable to see the England international playing in a Bournemouth shirt rather than that of Arsenal, especially on this form.
Wilshere had a few games out of Bournemouth's starting line-up of late, but here he was dictating the play and making life awkward against the League leaders.
Whenever given time and space, the 25-year-old was sublime in possession - finding the gaps in between Chelsea's defence and midfield.
The visitors had an early warning when he sent Harry Arter through with a lovely pass but the latter failed to keep his composure.
It was no surprise that Wilshere played a part in Joshua King's goal just before half-time, finding Benik Afobe in space to launch the counter.
Wilshere has just 14 months left on his current deal at Arsenal and the north London club shouldn't let such a talent slip through their fingers.
Flip of a coin between Kante and Hazard for Player of the Year
It seemed appropriate that Chelsea's two best players combined for their second goal - they have been leading the way for Antonio Conte all season.
A few weeks ago, N'Golo Kante looked a clear favourite to be honoured by the PFA and FWA for his outstanding performances this term.
At £32million, he represents ridiculous value in the transfer market and is regarded as one of the leading midfielders in the world.
Few on the planet are as entertaining as Eden Hazard though and he scored another sublime goal here.
It took his tally for the League season to 14 - matching his personal best and England great Paul Gascoigne will have appreciated the manner in which he took it, watching from his seat in the stands.
The Belgian has been finding the net in some key games during the run-in, including against West Ham, Arsenal, Manchester City and now here.
It is certainly a tough choice and it could go down to the wire, just like the title race.
Chelsea must improve defensively to win Double
There are a lot of statistics that Conte will be proud of from his first season in English football, but Chelsea's current defensive record won't be one of them.
The Blues' run of conceding just two League goals in 12 games after switching to a 3-4-3 formation in October is a distant memory.
They have now gone nine successive matches in the top flight without holding the opposition scoreless.
That is the worst run since they were struggling under beleaguered former boss Andre Villas-Boas in the 2011-12 season.
Chelsea will blame misfortune on this occasion. Simon Francis clearly handled the ball in the build-up to King's strike, which also deflected off David Luiz.
But the fact Bournemouth beat Thibaut Courtois didn't come as a surprise because Chelsea looked vulnerable on so many occasions.
Of course they are still seven points clear of Spurs and strong favourites to win the League.
But they won't want to be as porous as this when they face Spurs, who are in fine form, in the FA Cup semi-final in two weeks' time.
Costa's form remains a concern
Antonio Conte can deny it all he wants, but Costa's displays must be worrying him.
He has netted just three times in 11 League games in 2017, a complete contrast to the 14 in 18 before that.
The omens didn't look good during the pre-match warm-up when he completely shanked a shot during the training drill out of the Vitality Stadium.
It set the theme of Costa's day as he consistently fluffed his lines as Bournemouth keeper Artur Boruc loomed into view.
Granted it was his mishit effort, which took a wicked deflection and was subsequently credited to Francis, that opened the scoring.
But he should have beaten Boruc himself during the 90 minutes and ensured he brought up the landmark of a 50th Premier League goal.
There were many other opportunities for the Spain international to do that though, but he just didn't take them.
Arguably the worst of the lot followed some fine centre forward play, but when Marcus Alonso's cross came in he somehow missed the ball when standing a few yards out.
Chelsea will just hope that Costa rediscovers his mojo in the seven League games remaining or for the FA Cup clash with Spurs.