Carlos Tevez delivered the Citizens with a hat-trick while Aleksandar Kolarov and David Silva contributed a goal apiece as well.
The Citizens will learn who their opponent is for the semifinal round at Wembley Stadium tomorrow evening.
Here are six things we learned from City's impressive victory at the Etihad Stadium on Saturday.
Carlos Tevez was handed his second start in six days for Manchester City and he once again rewarded Roberto Mancini with a tremendous goal-scoring effort.
After scoring the only goal in City's win over Aston Villa on Monday, the Argentinian forward scored a hat-trick against Barnsley.
With Tevez back in the starting 11, City has looked like a more complete team.
At this moment, there is no reason not to select Tevez for the starting 11 as he has scored five goals in his last three games.
Lost in the remarkable offensive display on Saturday was the fourth consecutive clean sheet kept by Costel Pantilimon in FA Cup action.
In four FA Cup matches, Pantilimon has made 18 saves with seven of them coming against Stoke City in the fourth round.
Much of the credit for City's clean-sheet streak must be given to the entire team, not just Pantilimon.
City's back four have played four strong matches and their performances have been somewhat lost in the mighty offensive displays by the Citizens in the FA Cup this season.
Manchester City has benefited from playing three clubs from the Championship in the FA Cup this season.
While their bitter rival Manchester United has played clubs from the EPL in four consecutive rounds, City has only been drawn against one EPL side—Stoke in the fourth round.
City does not have any control in determining who they face in the competition and the argument can be made that they beat who they were drawn against and that is it.
However, there will always be critics out there who say that City's road to the semifinal round has been too easy and that they will be in for a shock when they go up against EPL opposition in the competition.
While critics will always have their own specific opinion about the club, all Manchester City can do is continue to win matches and try to diffuse the critics in the process.
Up until the final whistle, Edin Dzeko showed plenty of effort in the Manchester City attack.
Dzeko continuously made runs in towards the penalty area in an attempt to earn the sixth City goal of the match.
Unfortunately for the Bosnian forward, his efforts did not reward him with a spot on the score sheet.
While Dzeko's effort may be overlooked by many, his play late in a match that was over by the 30th minute is something that should be recognized.
Manchester City lined up in a 4-2-3-1 formation against Barnsley and the front four players in the formation jelled perfectly in the first 45 minutes.
Samir Nasri, David Silva, Edin Dzeko and Carlos Tevez were able to pass the ball around to each other with ease against the weak Barnsley back four.
Before he was taken off in the 52nd minute, Samir Nasri turned in one of his best performances of the season.
The same can be said about Silva, who left the match in the 66th minute after scoring the fifth and final City goal of the match.
With Nasri and Silva on the wings, the City attack was able to create plenty of chances for Tevez, who lined up in the center of the attacking trio, and Dzeko, who started the match as the lone forward.
Regardless of the opponent, if City's front four are able to work together like they did on Saturday, their attack could be unstoppable.
Of all the final possibilities for the FA Cup this season, the most intriguing one left has to be the Manchester Derby.
Manchester City did their part to advance to the semifinals and Manchester United will have their opportunity to advance to the final four against Chelsea on Sunday.
Depending on what the draw decides, these two rival clubs could be facing each other at Wembley Stadium on May 11 with a trophy on the line.
If United defeats Chelsea, the two Manchester clubs will be the clear-cut favorites to make the final.
After having a lackluster League Cup final between Swansea City and Bradford City earlier this season, no other possible final pairing would draw the hype and excitement that the Manchester derby would.
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