Tevez put his off-the-field police problems behind him at the Etihad Stadium as he scored three times, adding to goals from Aleksandar Kolarov and David Silva, to help City on their way to Wembley.
Roberto Mancini's side are still yet to concede a goal in the competition this season and always looked likely to go on and win the game when Silva's shot came back off the post and Tevez steered in the rebound after 11 minutes.
Tevez then turned provider as his cross found Kolarov to strike a low shot into the bottom corner, before the Argentinian scored his second four minutes later from close range.
Barnsley could not cope with the movement of the Premier League champions as City passed David Flitcroft's side, currently bottom of the Championship, off the park.
Tevez completed his hattrick five minutes into the second half when he steered Samir Nasri's cross into the bottom corner and played a vital part in the final goal as he provided a cross for Silva, who put the ball in the back of the net after his initial effort was saved.
A triple substitution from Barnsley almost resulted in a consolation goal as Jacob Mellis' half-volley was well saved by Costel Pantillimon before Manchester United loanee Ryan Tunnicliffe saw a low shot saved by the legs of the City keeper, while James Milner saw a late shot come back off the post.