Tevez, the Manchester City forward, put Diego Maradona's men ahead with a glancing header in the 27th minute but it was laced with controversy after replays showed he came from an off-side position.
Mexico protested to no avail as the issue of a lack of video technology reared its ugly head for the second time in as many games to heap further embarrassment on Fifa president Sepp Blatter.
But Javier Aguirre's side only had themselves to blame for gifting Argentina their second goal when Ricardo Osorio's woeful lapse allowed Higuain to notch his fourth goal of the finals before Tevez showed his class with a thumping drive into the top corner seven minutes into the second half.
Mexico had refused to be intimidated by their more illustrious neighbours and started brightly, tearing into tackles and breaking quickly when in possession.
Indeed, the underdogs could have taken the lead inside the opening eight minutes but Carlos Salcido's thumping 40 yard drive came back off the crossbar, Andres Guardado then blazed inches wide and Javier Hernandez also failed to hit the target.
But things started to unravel for Javier Aguirre's side before half time when Tevez put Argentina ahead in controversial circumstances. His initial challenge on Oscar Perez saw the ball rebound kindly to Lionel Messi, who lifted the ball back into the danger zone and Tevez headed into an open goal despite appearing to come from an off-side position.
Mexican players surrounded the referee after replays on the big screen justified their complaints, but the goal was allowed to stand and Aguirre's players then shot themselves in the foot by gifting a second goal to Higuain just five minutes later courtesy of Osorio's terrible blunder.
There were ugly scenes at half time when players and coaches from both sides clashed in the tunnel after Mexico continued their objections to Tevez's opening goal.
But Tevez had the last laugh with his second of the night when he smashed an unstoppable drive into the top corner on 52 minutes.
Javier Hernandez pulled one back on 71 minutes to offer Mexico a glimmer of hope but it proved nothing more than a consolation as Maradona's men cruised through.
Argentina (4-3-3): Romero; Burdisso, Demichelis, Otamendi, Heinze; Di Maria (Gutierrez 79), Mascherano, M Rodriguez (Pastore 85); Messi, Higuain, Tevez (Veron 69).
Mexico (4-3-3): Perez; Rodriguez, Salcido, Marquez, Osorio; Juarez, Torrado, Guardado (Franco 61); Giovani, Hernandez, Bautista (Barrera 46).