Jurgen Klinsmann wanted a response after his side lost to Costa Rica on Friday but was made to wait until after the break for the deadlock to be broken in Columbus.
A mistake by Mexico goalkeeper Jesus Corona allowed Eddie Johnson to ease American nerves and fire them in front on 49 minutes.
Experienced forward Landon Donovan sealed the victory 11 minutes from time when he converted Mikkel Diskerud's cross.
The home side could even afford to miss a penalty when former Spurs striker Clint Dempsey sent his spot kick wide in stoppage time.
The win lifts them a point clear at the top of the CONCACAF qualifying group and ensures they will finish in one of the three automatic qualifying spots.
Costa Rica, meanwhile, also booked their ticket to Brazil despite failing to grab victory against Jamaica in Kingston.
Randall Brenes capitalised on some hesitant Jamaican defending to fire the visitors in front in the 73rd minute.
However, Jermain Anderson popped up with the equaliser in injury time to secure a dramatic point for bottom-placed Jamaica.
Costa Rica's despair quickly turned to joy when news filtered through of Honduras' 2-2 draw with Panama, which means Jorge Luis Pinto's side are assured of a top-three place with two games remaining.
Honduras remain in third, three points clear of Panama and Mexico, with games against Costa Rica and Jamaica to come.