Diego Godin had a goal disallowed in the first minute of the match for the hosts after finishing from close range, but a foul was spotted by the assistant referee leading up to the goal.
Grandsir did open the scoring for Monaco in the 18th minute after Radamel Falcao’s cut back into the area forced an error at the back, which allowed the French striker to pounce on a loose ball.
Diego Costa levelled matters for the home side in the 31st minute following a clever flick from Antoine Griezmann inside the box, 1-1.
Leonardo Jardim’s troops were stretching Atletico on the wings as the half continued but their final ball into the area was not up to standard.
Jose Gimenez gave Simeone’s charges the lead in stoppage time of the first half with a towering header inside the box following a corner, 2-1.
Costa thought he had got his brace and for the visitos six minutes after the break tucking home a flicked header from Griezmann at the far post but he was flagged offside.
Monaco had a strong penalty claim in the 66th minute after Falcoa appeared to have been fouled inside the area but the referee was not interested.
The French side were struggling to create clear chances in the second half against a resilient Atletico defensive line.
The Costa and Griezmann combination upfront was a problem for Monaco whenever they ventured forward, but they were unable to add to the scoreline as the encounter 2-1 in favour to the LaLiga outfit.