Gimenez picked up the pieces at a 78th-minute corner to drill home the opener, before Diego Godin's strike in the aftermath of a free-kick five minutes later deflected in off former Real Madrid man Cristiano Ronaldo.
Alvaro Morata had earlier been denied a goal against his old club by VAR, while Juve's best chance saw a Ronaldo free-kick tipped over by Jan Oblak in the first 10 minutes.
The Serie A champions looked on course to take a goalless draw back to Turin until Atleti, who will have Diego Costa and Thomas Partey suspended for the return trip, snared the victory.
95' | 2-0 | FULL-TIME at the best stadium in the world!— Atlético de Madrid (@atletienglish) February 20, 2019
Our team earns a fantastic 2-0 win.
Thank you Atléticos for your mind-blowing support tonight... You were incredible
#AúpaAtleti #UCL pic.twitter.com/BxLXV8f9o5
A feisty first half saw Atleti appealing for a penalty after a minute. Blaise Matuidi caught the boot of Antoine Griezmann as he challenged for a chest-high ball, but the referee ignored the protestations of Diego Simeone's men.
Ronaldo then drew an impressive save from Oblak with a 30-yard free-kick in the seventh minute, but only after Costa had ruled himself out of the second leg by encroaching at the set-piece.
Leonardo Bonucci headed over a glorious opportunity from a corner before a low Partey drive gave Wojciech Szczesny his first assignment of the evening.
Atleti were awarded a penalty for a challenge on Costa after 27 minutes but the decision was changed to a free-kick outside the box on review. In truth, the striker was fortunate to avoid a second booking for diving after going down under the softest of touches from Mattia De Sciglio on his shoulder.
Juanfran was lucky to escape punishment when his studs raked the ankle of Ronaldo. The former Real forward found sympathy in short supply but appeared to remind Atleti fans of his five Champions League titles by raising five fingers soon after.
A disappointing evening for Costa continued when he side-footed well wide after being sent through on goal, before Szczesny pulled off a sensational save to tip a Griezmann lob onto the crossbar.
Costa was replaced by Morata before the hour mark and the ex-Juve striker looked to have put Atleti in front with a header until he was found, via VAR, to have pushed Giorgio Chiellini in the build-up.
But Atleti's goal heroes came from their defensive line, with Gimenez netting his second of the campaign before Godin scored his first Champions League strike since October 2014 to leave Juve - denied a response when Oblak blocked a fierce Federico Bernardeschi drive - with work to do on home soil next month.
What does it mean? Advantage Atleti
Juve were favourites for this tie when the draw was made but if they are to progress any further in this tournament, they are going to have to work hard for it. Atleti knew they had to make home advantage count to compete over the two legs and they showed great spirit to keep going and snatch the win late on.
A win made in Uruguay
These two sides looked like cancelling each other out until Atleti's centre-backs decided to get involved at the other end of the pitch. Gimenez and Godin are the first two Uruguayans to score in the same Champions League match in the history of the competition.
Costa treads a fine line
Fiery encounters can often bring out the worst in Costa and Wednesday was no different. A cheap yellow card for stepping out of the wall could justifiably have been followed by a second booking for making the most of a small touch on the shoulder from De Sciglio.
Key Opta Facts:
- The last five times Juventus have lost a Champions League first-leg tie of a knockout stage in European competitions, they have been eliminated.
- Juventus have lost two consecutive games in a single Champions League campaign for the first time since October 2014 (v Atletico Madrid and Olympiacos).
- Juventus have failed to score in a Champions League last-16 game for the first time since the 2008-09 campaign (0-1 v Chelsea).
- Atletico Madrid are the only side Juventus have faced at least three times against without finding the net.
- Each of Juventus' last four Champions League defeats with a two-plus goals margin was against Spanish opponents.
- Leonardo Bonucci played the 500th game of his club career.