Gimenez slid to the floor in a crowded penalty box to bundle the ball into the net from close range in the 78th minute, after former Juve forward Alvaro Morata had had a goal ruled out following a Video Assistant Referee (VAR) review.
Atletico also had a penalty awarded then taken away by the technology earlier in the game but only grew in determination and captain Godin grabbed a vital second goal in the 83rd minute to take into the return leg in Turin.
The veteran defender appeared at the near post to knock a loose ball into the net after Atletico wreaked havoc again from a set-piece, the shot deflecting off familiar foe Cristiano Ronaldo on its way in.
The meeting of two European juggernauts, who have reached four of the last five Champions League finals between them without lifting the trophy, was as bruising and tight a match as could be expected between sides renowned for their intimidating defences.
Juve's signing of Ronaldo was a clear attempt to boost their firepower and hopes of winning the competition but the man who scored 22 times against Atletico as a Real Madrid player was kept relatively quiet on his return to the Spanish capital.
RONALDO WHISTLED
The Portuguese tested Atleti keeper Jan Oblak early on with a scorching free kick and as his side chased an away goal in stoppage time he headed over the bar, prompting gleeful whistles from the home supporters at a raucous Wanda Metropolitano Stadium, which will host the competition's final in June.
Atletico had made a timid start and their best moment before the interval was when a bursting run from Diego Costa drew a foul by the area which was initially given as a penalty then reduced to a free kick.
Roared on by their famously fervent supporters and animated coach Diego Simeone, Atletico grew in confidence in the second half and should have taken the lead when a pass from deep by Antoine Griezmann released Costa, who rampaged towards the area but dragged his shot well wide of goal.
France forward Griezmann came much closer to scoring moments later but his attempted chip was turned on to the crossbar by Juve keeper Wojciech Szczesny.
That save did not halt Atletico's momentum and they were well worthy of the two goals although they must do without Costa and Thomas Partey, who are suspended from the second leg on March 12 along with Juve's Alex Sandro.
