By the end Chelsea were toying with their opponents and the Derby County fans who would probably rather forget the indignities of their last season in the Premier League, with a record low of 11 points, were reminded how brutal it can be against this kind of refined opposition.
They lost 6-1 against Chelsea that season and, though the latest defeat was nothing like as harrowing, José Mourinho's team made it a harsh history lesson during those moments in the second half when their domination of the ball turned into the hard currency of goals.
The gulf was considerable and the Championship team had to give everything to prevent any more damage beyond Mikel John Obi's 66th-minute header and the shot from Oscar, the game's outstanding's performer, that carried so much swerve and power to deceive Lee Grant in the Derby goal.
Fernando Torres menaced them after replacing Samuel Eto'o, whose performance merely reiterated his own decline, and it was just a pity for Chelsea that Ramires had to tarnish the occasion by becoming the latest Chelsea player to be caught diving.
He was booked, following on from Oscar's yellow card at Southampton on New Year's Day, and it represents an embarrassment to Mourinho bearing in mind it is only a week since he concluded his criticism of Luis Suárez for his "acrobatic swimming-pool jump" by proudly declaring his players would not resort to such tactics.
Mourinho would not budge an inch afterwards, pointing out they were "isolated incidents" rather than serial offending, but it was an unwanted sideshow and his argument has been diminished.
The bottom line was that Chelsea did not need to resort to anything underhand to guarantee their fourth-round tie against Stoke City. They had to withstand a spirited start from Derby and Steve McClaren was not being unduly generous when he said his players could be encouraged by their efforts. "Someone said to me we actually had more players in our squad than they do. I said: 'Yeah but look at the value.' One of theirs was worth as much as ours together."
At first that disparity was not always apparent. Eto'o's rotten first touch to spoil Chelsea's first real chance of note was not the only moment of carelessness from Mourinho's players in the opening 20 minutes. That was the point, however, when Oscar emerged as the most influential player on the pitch. Two of his long-range efforts went close and the opening half finished with Ramires's shot taking a slight deflection to skim against a post.
At half-time Mourinho was not entirely happy. "We didn't play badly," he said. "We played quite well but still 0-0 at half-time is a big risk because in the second half, if the opponent scores one, you are in trouble."
Yet this was not an occasion when Will Hughes, Derby's talented but raw midfielder, demonstrated why he is attracting so much interest from Premier League clubs. The 18-year-old looked lightweight and Mourinho took advantage by withdrawing one of his own central midfielders, Michael Essien, to leave Mikel as a lone anchor man and spring Eden Hazard from the bench. Once again a Chelsea victory can be largely attributed to Mourinho's talent for changing his team mid-match.
Hazard's introduction immediately coincided with their best period of the match and Derby were already looking vulnerable by the time Jamie Ward brought him down for the free-kick that led to the opening goal. Mikel, making his 300th Chelsea appearance, had been handed the captain's armband when Essien went off – Mourinho later said it should have gone to Ashley Cole – and the ball flashed off his forehead for only his fourth goal in eight seasons at the club.
There was a period after Grant had let in Oscar's shot when it suddenly looked as though Derby's afternoon might turn into an ordeal. Torres danced round Jake Buxton and went past Grant but was crowded out before being able to apply the finishing touch. In the next attack the Spaniard ran clear again and drove his shot against Grant's legs. Derby were largely holding on before a brief, late flurry of their own, with Chris Martin's left-foot shot probably ranking as their best effort of the match.
The dive from Ramires, running beyond Michael Keane, came between the goals and what a strange twist of irony that this was the referee, Andre Marriner, who had been officiating when the same player went to ground and won a highly contentious penalty against West Bromwich Albion at Stamford Bridge in November.
"The last time [with Oscar] I was happy with the card and I was happy with Oscar's justification of the situation," Mourinho said. "This time I didn't speak with Ramires but Marriner was so close, if he made that decision it was because he was right.
"I maintain [we have no divers]. You will see when Oscar dives again and you will see when Ramires will be booked again. In other clubs there are really divers. If you want to look for players doing it every weekend, it's very easy. Sit in front of the television and you will find them. We do the opposite." Ramires, one imagines, should expect the point to be made very matter-of-factly.