Mexico, a six-time Gold Cup champion going for its third straight title, will face Panama in the semifinals on Wednesday in Dallas.
Panama upset Mexico 2-1 in a group match earlier this month.
Jimenez used his right foot to redirect Miguel Layun's shot attempt from the right side with a sweeping move that helped the ball sail just past diving goalkeeper Jan Williams and into the left corner of the net.
Three of Mexico's 11 shots in the first half were on goal, but Williams only had to dive once to make a save. The other two attempts went right into his hands.
In the 62nd minute, Layun attempted a shot from the right top corner of the box. His arc looked to be on line before Williams stretched out to deflect the ball high.
Barely 1 minute later, Williams tipped away a shot by Jimenez, but he couldn't prevent him from scoring the winning goal with about 5 minutes remaining.
Williams faced 23 shots. Mexico goalie Jonathan Orozco faced seven.
Mexico improved to 5-3-8 in international play this year.
NOTES: CONCACAF officials announced a crowd of 54,229, a soccer record at the 21-year-old Georgia Dome. ... Mexico improved to 12-3-3 against Trinidad and Tobago, including a pair of wins in the Gold Cup. This was the first meeting between the teams in a knockout round.