A lot of the focus heading into this clash at Stamford Bridge was on the lack of goals Chelsea's strikers have scored this season in comparison to Liverpool's Luis Suarez.
The Uruguayan—along with Hazard, whose excellent display was a major factor in Chelsea coming away victorious—was forced to play second fiddle to Eto'o, though, with the Cameroon striker not only scoring the game's winning goal but also being involved in two major talking points.
The first came within the opening three minutes—a needlessly high tackle on Jordan Henderson going unpunished when Chelsea could have had little complaint had Eto'o received his marching orders.
Liverpool's resulting free-kick saw Martin Skrtel latch on to a Suarez knockdown to open the score, a fact that probably reduced the Reds' sense of injustice when it came to Howard Webb's decision not to book Eto'o at least.
Brendan Rodgers' side were left to rue Webb's leniency on 30 minutes later when who else but Eto'o stepped up to put Chelsea 2-1 in front after Hazard had earlier pulled them level.
"I didn't see [the first incident]," replied Jose Mourinho when asked for his reaction to Eto'o's tackle on Sky Sports.
"I think Samuel is a new player in the Premier League. I criticize him internally a lot because of his difficulty to adapt to what the Premier League is in terms of aggressivity and physicality, so if he had a tackle deserving a card, it's my fault because I am asking him to adapt quickly."
It was a diplomatic response from the Blues manager in his attempts to deflect any criticism from his player.
That said, Eto'o can hardly be absolved of any blame. His challenge on Henderson was reckless and had it happened later in the game, the punishment may have been far more severe.
When Mourinho has the opportunity to see the incident for himself, he must surely agree.
The Portuguese manager was somewhat more condemning of Suarez, who he claimed should have been booked himself for his attempts to win a penalty.
The incident came late on as Liverpool chased a result, with Suarez appearing to be knocked to the floor by Eto'o as he pursued Cesar Azpilicueta to win back possession.
It happened in full view of the referee and in the penalty box, although play was allowed to go on with Eto'o again finding himself fortunate.
"I would resolve these situations very easily," Mourinho explained. "A yellow card for Luis Saurez because I keep saying I hate players who try to provocate situations, the same way I say Luis is an amazing player and I have a lot of respect for his quality and his attitude to win every game.
"He's an amazing player, but he tries too much to provocate these situations [...] Eto'o puts his body in front and Suarez, it looks like someone has shot him in the back, and for me that's a clear yellow card."
Despite the negative headlines that will follow on the back of this win, Mourinho will be happy that for once they are not about a striker struggling to find the back of the net.
For too long that line has been rolled out, with the Blues coming in for plenty of justified criticism.
Not on Sunday, though.
Eto'o was preferred to Fernando Torres and, controversy aside, did his manager and teammates proud with an accomplished display.
His goal represented excellent forward play, too, doing enough to lose his marker, gaining a yard on Skrtel before prodding beyond Simon Mignolet.
Coming with just shy of an hour still to play, Mourinho would have preferred the goal not to be Chelsea's last of the game.
There were moments when some poor attacking decisions meant the Blues were unable to make their lead more comfortable, but they did enough to see out the 90 minutes and record a much-deserved three points.
A Chelsea striker scores a vital, winning goal. The last time we could utter those words was on the back of Torres' dramatic winner against Manchester City in October.
It's a step in the right direction for the Blues. They're yet to hit their best form, but sitting third in the table and two points off the top, Mourinho and his men have every reason to be happy with themselves right now.
Garry Hayes is Bleacher Report's lead Chelsea correspondent and will be following the club from a London base throughout the 2013-14 season. Follow him on Twitter here @garryhayes