Some calamitous defending from 10-man Tottenham, who had Younes Kaboul sent off, helped the hosts move seven points clear at the top of the Premier League
After a goalless first half, the Cameroon striker capitalised on a mistake from Jan Vertonghen to put Jose Mourinho’s men in front in the 56th minute before Younes Kaboul brought down the forward inside Spurs’ box to concede a penalty.
The French defender was given a straight red card for his challenge, while Hazard converted the spot kick to register his 13th Premier League goal of the season before two late goals from Ba sealed the win in some style.
Eto'o was immediately at the heart of the action following his late call-up after Fernando Torres was injured in the warm-up.
Hazard released the striker inside the first 30 seconds and Tottenham goalkeeper Hugo Lloris tore out of his area to bring Eto'o down. An offside flag, which appeared to be incorrectly raised, possibly saved the France international from an incredibly early red card.
Lloris' haphazard start continued in the fifth minute when Eto'o returned the favour to Hazard and the playmaker negotiated a rash lunge from the visiting keeper but shot wide when off balance.
Tottenham could have moved ahead in the 14th minute as Nabil Bentaleb collected Emmanuel Adebayor's flick on, only to drag past the post with frustrated team-mates queuing up in the box.
Petr Cech got down superbly to beat away a rasping volley from Sandro, while Eto'o drilled beyond the near post after being forced wide by Kaboul - one of four players recalled by Tottenham boss Tim Sherwood.
Mourinho sent on Oscar for the yellow-carded Frank Lampard at the break and there were soon chances at both ends - Kaboul rising highest to head a corner into Cech's arms before Andre Schurrle missed his kick having linked nicely with Eto'o.
Vertonghen also tried his luck with an audacious 30-yard chip but a dreadful error from Tottenham's left-back allowed Chelsea to open the scoring.
The Belgium international lost his footing and saw his subsequent pass intercepted by Eto'o, who bore down on goal and finished incisively.
Kaboul then bundled Eto'o over as the latter looked to meet Hazard's low cross. Referee Michael Oliver, adjudging the defender to have prevented a clear goalscoring opportunity, produced a red card and Hazard nonchalantly stroked home the spot kick, sending Lloris the wrong way.
Sherwood finished the game without both starting centre-backs after Michael Dawson departed with a hamstring injury, and his team ended the contest in disarray.
Sandro fell when trying to retrieve Oscar's right-wing cross, allowing Ba to finish in the 88th minute and the same player capitalised once more when an inexplicable back header from Kyle Walker sold Lloris short.