Facing the real prospect of failing to qualify for the first time since 1990, Mexico moved back into contention after Jimenez's spectacular goal at the Azteca Stadium.
Just moments after Luis Tejada had equalised for Panama, sending the crowd into a state of despair, Jimenez produced a perfectly executed bicycle kick on the edge of the box to give his team victory after Oribe Peralta's first half strike.
"Sometimes you just have to find a way to score a goal," said Jimenez, speaking to ESPN through a translator.
The dramatic result moved Mexico into fourth place in the six-nation CONCACAF standings on 11 points with one round of matches to go.
The top three teams qualify automatically with the fourth advancing to a two-leg playoff against Oceania winners New Zealand.
Honduras occupy the third spot on 14 points and need just a draw in their final game on Tuesday against Jamaica to clinch their spot in Brazil.
Honduras striker Jerry Bengtson scored the only goal of the match midway through the second half to clinch the victory at the Olympic Stadium in San Pedro Sula and setting off wild celebrations in the country.
The streets of Tegucigalpa and San Pedro Sula were filled with people celebrating and waving the blue and white flag of Honduras with the knowledge they had at least secured a playoff spot before Mexico played Panama.
"I want to congratulate the boys of the national team for their win today," Honduras President Porfirio Lobo told reporters.
"This shows that Hondurans can do it when we decide to do it. We are going to Brazil! Long live Honduras!"
The result kept Honduras three points clear of Mexico in the battle for CONCACAF's third and final automatic spot.
Mexico only need a point from their final match against Costa Rica to be assured of getting the playoff spot.
They can claim the last automatic berth if they win and Honduras lose to Jamaica, who have not won a game in the final round of qualifying.
"This was a very important victory for the team" Mexico captain Rafael Marquez said.
Traditionally the strongest team in the CONCACAF region that covers North and Central America and the Caribbean, Mexico have qualified for every World Cup since 1982, with the exception of 1990 when they were banned by FIFA after fielding over-age players in a youth tournament.
But they have struggled to score throughout their latest qualifying campaign, finding the net just four times in their first eight matches, and are now on their third coach.
Jose Manuel 'Chepo' de la Torre was dismissed after a 2-1 home defeat by Honduras then his replacement, Luis Fernando Tena, stepped down after one game in charge when Mexico lost to the United States.
With Victor Vucetich having taken over the reins, Mexico looked more threatening against a Panama side that has never qualified for the World Cup but are on a high after reaching the final of this year's CONCACAF Gold Cup.
Peralta gave the home team the lead after 40 minutes when he chipped the ball over Panama goalkeeper Jaime Penedo.
Mexico might have another goal in the second half when Javier Aquino was pulled down in the box by Harold Cummings and the referee pointed to the spot.
But Mexico's Manchester United striker Javier Hernandez failed to convert the chance when a sprawling Penedo guessed correctly and dived to the left to save the shot.
His miss looked even more costly when Tejada got in behind the Mexican defence and poked the ball into the net.
But just four minutes later, Mexico replied with a goal destined to be an instant internet hit as Jimenez, with his back to the goal and two defenders on him, flicked the ball into the air then flipped himself over and whacked it into the net.
The United States (19) and Costa Rica (15) occupy the first two places and have already qualified for Brazil.
Honduras are already assured of at least a playoff spot, against the Oceania winners New Zealand and only need a point from their final match against Jamaica on Tuesday to reach the finals for the third time and the second in a row.
Jamaica are yet to win a match in the six-nation final round of qualifying and have no chance of advancing to Brazil after losing 2-0 to the U.S. in Kansas City on Friday.