With suspended coach Gerardo Martino watching on from the stands at State Farm Stadium, Mexico were frustrated by the minnows on Tuesday.
It was unable to create much of note through 90 minutes, but found a breakthrough early in extra time through a Jimenez penalty.
After a soft spot-kick was awarded, Jimenez stepped up to send 10-time champions Mexico into the decider.
Mexico struggled to create clear-cut chances throughout the first half as Haiti defended desperately.
Roberto Alvarado fired a decent opportunity wide in the 10th minute before Jimenez put an effort over the crossbar from close range.
Haiti was well-organised and frustrated Mexico, who struggled to put shots on target in the opening 45 minutes.
Jesus Gallardo and Jonathan dos Santos missed the target with efforts, while Jimenez forced a relatively comfortable save from Johny Placide with a 35th-minute header.
Haiti also had its moments, threatening early in the second half as Frantzdy Pierrot fired wide on the turn in the 49th minute.
Andres Guardado was the next to threaten for Mexico, his curling 20-yard free-kick tipped over by Placide, whose last-ditch tackle later denied substitute Uriel Antuna.
Forced to extra time, Mexico finally found their breakthrough in somewhat controversial fashion through Jimenez.
The forward went down in the area under the slightest contact, before stepping up to convert from the penalty spot.
Haiti's brave effort went to the end as they almost stunningly equalised in the 119th minute, Mikael Cantave's 20-yard strike hitting the crossbar with Mexico goalkeeper Guillermo Ochoa beaten, while Luis Montes missed an open goal at the other end.