The Argentina striker also played a part in goals by Aleksandar Kolarov and David Silva as City crushed Barnsley 5-0 to reach the semifinals.
Tevez helped to secure City's biggest win of the season while out on bail after being arrested for driving with a suspended license. The maximum punishment is six months in prison.
"It is his problem — not ours," City manager Roberto Mancini said before quipping, "If it has this effect on him I hope the police can stop him every day."
Wigan will also be playing at Wembley next month after reaching the semifinals for the first time in its 81-year history by beating Everton 3-0.
But it was a bittersweet day for Wigan as the team was sucked back into the Premier League relegation zone after Aston Villa won 2-1 at Reading.
With a game in hand, Wigan is three points behind Villa, but a point above both Reading and bottom-place Queens Park Rangers, which beat Sunderland 3-1.
The tight relegation tussle is in contrast with the title race where Manchester United is 12 points ahead of City but in cup action on Sunday when it hosts Chelsea in the quarterfinals.
The cup is City's last realistic chance of winning a title this season, and Mancini's side has reached the semifinals without conceding a goal.
Tevez took just 11 minutes to open the scoring against second-tier club Barnsley.
After David Silva's strike was pushed onto the post by goalkeeper Luke Steele, Tevez was on hand to bundle in the rebound.
Tevez turned provider in the 27th, with Kolarov meeting his cutback to double City's lead.
Tevez was on target again four minutes later from close range after connecting with Silva's pass.
And the hat trick was completed five minutes into the second half after being set up by Samir Nasri.
Tevez was also involved in the buildup that saw Silva score after being denied initially by Steele.
"(The early goal) made a big difference because when you play against that kind of team you need to knock them down from the first minute, which we did and after that they lost confidence," Mancini said.
For Wigan, topflight survival, rather than cup success, is the priority for owner Dave Whelan. But a trip to Wembley will give him happier memories of the national stadium after seeing his own career end there when he broke his leg playing for Blackburn in the 1960 FA Cup final.
"It has been an absolutely wonderful day. In the first half we skinned Everton alive," Whelan said. "I had a dream in the week we came to Everton and beat them and then got Blackburn, who beat Millwall (on Sunday), in the semifinal.
"We're halfway there. I hope it comes true and I'd love to go to Wembley and play Blackburn."
Wigan's goals came inside a four-minute span in the first half.
Maynor Figueroa headed in the opener at Goodison Park in the 31st minute from Jordi Gomez's corner.
Callum McManaman was on target a minute later after outsprinting Sylvain Distin before striking past goalkeeper Jan Mucha, who was filling in for the injured Tim Howard.
Gomez completed the scoring from outside the penalty area after latching onto Arouna Kone's pass.
"For us as a football club to go to Wembley is a unique moment — an historic moment," Wigan manager Roberto Martinez said. "We want cup success, but not at the expense of the league form."
Six of the bottom eight played on Saturday.
QPR has back-to-back wins for the first time this season, and is four points from safety by beating Sunderland.
After Steven Fletcher put Sunderland in front at Loftus Road, Loic Remy levelled before half time and Andros Townsend and Jermaine scored with exquisite half-volleys for the hosts.
QPR is level on points with Reading but remains bottom because of fewer goals scored.
Reading had gone ahead against Villa after Nathan Baker's 32nd-minute own goal but Christian Benteke equalized inside two minutes.
And Gabriel Agbonlahor clinched the win for Villa, which is just above the relegation zone, three points ahead of Wigan, which has a game in hand.
Southampton is a point ahead of Villa after drawing 0-0 at Norwich, whose striker Grant Holt had a stoppage time penalty saved by Artur Boruc.
West Bromwich Albion rose to seventh by fighting back to beat Swansea 2-1.
Lukaku cancelled out Luke Moore's opener before halftime and Swansea midfielder Jonathan de Guzman inadvertently turned the ball into his own net in the 61st at the Hawthorns.Suggest a correction