Defending champion Chelsea broke Brentford's resistance with a potent second-half attacking display to beat the third-tier club at the second attempt with a 4-0 win.
Held by Brentford three weeks ago, Chelsea couldn't find a breakthrough until the 54th minute of the fourth-round replay when Juan Mata struck from the edge of the penalty area.
Oscar found the net for the second time in four days, Frank Lampard side-footed in his 199th Chelsea goal, and captain John Terry headed in the fourth.
Chelsea will play at Middlesbrough on Feb. 27 in the fifth round to decide who plays the winner of Monday's match between Manchester United and Reading.
Man City is already through to the quarterfinals, in which it will play Barnsley, after thrashing second-tier club Leeds 4-0.
Yaya Toure put City ahead after five minutes before Sergio Aguero scored from the penalty spot, helped to set up Carlos Tevez's goal after the break and then collected his second.
Huddersfield spared the blushes of lower league teams, slightly, by at least scoring in a 4-1 loss to Wigan, although the second-tier club was already 3-0 down by that stage.
The only Premier League fixture this weekend managed to eclipse the cup for goals, with Liverpool hammering Swansea 5-0.
The cup shocks came on Saturday with second-tier club Blackburn winning at Arsenal and third-tier team Oldham holding Everton. In the quarterfinals next month, Everton or Oldham will host Wigan, and Blackburn will play Millwall in an all-League Championship encounter.
Just how lucrative a cup run can be to lower-league teams was highlighted by Brentford estimating that it has earned more than $1 million from the two fourth-round matches against Chelsea.
The seventh-place team in League One did manage to repel waves of attacks by Chelsea with a disciplined display in the first half, and even found the net through Marcello Trotta. But the referee had already blown for a foul on Brentford midfielder Adam Forshaw.
Chelsea's finishing was wayward in the first half, although Oscar did hit the post. After the break, the intensity was raised — and Brentford paid the price.
Goalkeeper Petr Cech launched the ball forward, Demba Ba held off the Brentford defence, and Mata picked up possession before crisply striking into the net.
The second was even slicker from Oscar in the 68th.
Eden Hazard, who had just replaced Victor Moses, seized possession near the halfway line and powered into the penalty area where he sent the ball to Branislav Ivanovic. The right back cut the ball back to Oscar, who flicked it into the net through three defenders.
Chelsea took just three further minutes to make it 3-0. Mata broke down the left flank and squared the ball for an unmarked Lampard to volley home.
The 34-year-old midfielder's 199th goal puts him three behind Bobby Tambling's club record, however he hasn't been offered a new contract beyond the end of the season.
Another member of Chelsea's old guard found the net in the 82nd, with Terry meeting Oscar's cross.
"They made it very difficult," Terry said. "(They had) two banks of four and sat very deep."
At Etihad Stadium, a City win seemed certain after neat link-up play between David Silva, Tevez and Yaya Toure led to the latter rounding goalkeeper Jamie Ashdown and scoring.
Aguero was on target from the spot in the 15th after tangling with Tom Lees.
The Argentina striker provided the cross seven minutes after the break that Tevez tapped in at the far post. And Aguero found the net again in the 74th after latching onto Silva's high, defence-splitting pass, and curling past Ashdown off the post.
At Huddersfield, Wigan reached the quarterfinals for the first time in 26 years.
Callum McManaman and Arouna Kone scored in the first half and James McArthur struck early in the second half for Wigan.
Although Huddersfield substitute Lee Novak headed one back in the 62nd, Kone went on to power in his second in the 89th.
At Anfield, the League Cup was on Swansea's minds as several key players, including top-scorer Michu, were left on the bench ahead of next Sunday's final against Bradford.
The weakened side collapsed after Steven Gerrard's spot kick beat goalkeeper Michael Vorm in the 34th minute after Luis Suarez was fouled by Kemy Agustien.
Just 16 seconds into the second half, Phillippe Coutinho marked his debut by going through the Swansea defence before beating Vorm.
Inside five minutes, Liverpool was further ahead after Jose Enrique poked the ball into the net from Daniel Sturridge's pass.
Suarez went through past the Swansea centre backs before firing in the fourth and, after Wayne Routledge handled, Sturridge netted Liverpool's second penalty in the 71st.Suggest a correction