So, rather than trebles it's doubles, as a single N'Golo Kante goal was enough to subject Jose Mourinho to a second successive defeat at his old club and keep Chelsea on course for both the Premier League and FA Cup.
Antonio Conte's side go into the semi-finals powered by some of the notable anger of this match in its early stages, and having completely commanded the majority of this FA Cup sixth-round win over Manchester United, which ended the visitors' hopes of winning three cups.
Mourinho will have the excuse of the Ander Herrera's red card from those rancorous opening exchanges and the absence of Zlatan Ibrahimovic but, at this point, it seems there's always an excuse when there's yet another setback.
The game really highlighted a fair few disparities between the squads and why Chelsea are top and United sixth, as the home side could have ended up winning by a lot more against a generally unambitious side.
Victor Moses was doing so much more than a relative United counterpart like Matteo Darmian and, most of all, match-winner Kante showed Paul Pogba what a real value-for-money performance was. There was also the fact that Herrera's red was probably a consequence of United's primary game-plan in shackling Chelsea's main playmaker, even if they can debate the nature of the second yellow card.
Either way, Chelsea were much the better team by the end.
If the build-up to this fixture was dominated by subtle mind games about who exactly plays counter-attacking football and what exactly constitutes that type of approach, the match started with two robust sides that created a lot of properly physical confrontations - and that occasionally threaten to spread to the benches. This had spark.
Mourinho has often been accused of lacking the required innovation in recent years, but his starting line-up was something rarely seen in the game: four centre-halves at the back, two effective wing-backs and an entire game-plan that seemed to be just about stopping Hazard.
With the spike of the occasion, it was perhaps inevitable that two players like Herrera and Diego Costa would come together early on, although they helped each other up in an endearing moment that was quite different from what was to come.
These early clashes still created enough space for some football, although mostly from Chelsea. United's best opportunity came from a punt upfield that looked to release Marcus Rashford - back in the team after Mourinho so pointedly said he was ill - with Henrikh Mkhitaryan then driving just wide.
It wasn't long until Hazard eventually got free, though. His supreme run and shot on 16 minutes almost opened the scoring, and temporarily saw Chelsea open up.
They laid siege for the next few minutes, with David de Gea pulling off the save of the game from an improvised Gary Cahill shot in the box, and a Marcos Alonso effort.
It wasn't going to be long, either, until it properly kicked off. With United players appearing to be on some kind of rota to tackle Hazard, the Belgian was caught by Herrera on 20 minutes.
A yellow card came out, and another warning had been offered. It was not heeded. With referee Michael Oliver now repeatedly telling players that he would show more cards, Herrera went in on Hazard with a more routine challenge on 35 minutes, the playmaker again going down. Oliver got a second card out, Herrera went off, and Conte aggressively celebrated as if it was a last-minute equaliser.
It was far from the only flashpoint on the sideline. Chelsea fans had been showing how much their attitude to Mourinho had changed by telling him where to go in obviously vulgar terms, leading to him holding up three fingers and pointing to the pitch to obviously highlight how many titles he'd won more, and the home fans to sing "it's all your fault", "you ruined it" among other vulgar offerings.
Moments later, after Alonso and Antonio Valencia had been involved in another head-to-head, Mourinho was straight over to the fourth official to complain, only for Conte to charge over and scream in his face. It was as if the Italian had been waiting for the opportunity. There were no subtle mind games here.
Oliver was unwilling to let it continue, however, and called both managers over for a talking-to.
Mourinho had probably made his own biggest statement by hauling off Mkhitaryan for Marouane Fellaini the second Herrera was sent off, making his game-plan now abundantly clear.
The necessity with this kind of approach and a mere 10 men on the pitch, though, is that you need everyone doing their job to the maximum.
The again subdued Pogba was not doing that; he got caught just after 50 minutes, and Kante caught the ball well to make it 1-0 from the edge of the box. In truth, the shot seemed to surprise both Pogba and De Gea - perhaps because this was just Kante's second goal for Chelsea and third in English football - but it was no surprise Conte's side were in the lead.
The pattern had been set since the red card. Mourinho looked as livid after the goal as he had done at any other point in the game.
Chelsea were by then in total command with a series of efforts - from Victor Moses to Costa - that went narrowly wide, although there was one big warning with the game still at 1-0 when Rashford too easily got free from Gary Cahill on the break, but then couldn't find the finish to beat Thibaut Courtois, who saved well.
Possibly alerted into action, though, there was an impressive mental sharpness about what Chelsea did thereafter. They supremely manipulated the space - and the extra man - to herd United into their own area like cattle. It's difficult to say whether frustration got the better of Mourinho's side once that started to happen, but a few challenges and fouls bore that hallmark.
Valencia went in with conspicuous aggression on Alonso, and at one point Pogba was resorted to just bundling Kante to the ground. It was the only time he could get near him, the only time he could get something on target. The world-record signing tried a shot close to the end of the game that could still have rescued United, only for it to go pitifully wide.
Mourinho won't win three trophies, but Conte can still win two, after beating United again. (© Independent News Service)
Manchester United manager Jose Mourinho has angrily snapped back at the Chelsea supporters who taunted him during his side’s 1-0 FA Cup quarter-final defeat, after insisting he is still the club’s greatest manager in a passionate post match press conference.