As has been the case in recent weeks, Zinedine Zidane had to travel with an extremely depleted squad to the Gewiss Stadium due to injuries. Isco was handed a rare start as the focal point of attack in the absence of Karim Benzema, while Vinicius Junior and Marco Asensio flanked him in attack.
Stand-in captain Raphael Varane made his 350th appearance for the Bernabeu outfit, and Toni Kroos also became the German with the joint-most appearances for the club.
The Real Madrid bench was less than stellar and had Mariano Diaz - himself on the fringes - as the only recognizable first-team player.
The game started on a relatively slow note, with neither side seizing the initiative, but the first talking point came in the 17th minute.
A quick break saw Ferland Mendy race through on goal before he was cynically brought down on the edge of the area by Remo Freuler. Referee Tobias Stieler wasted little time in reaching for his pocket to brandish a red card.
There were heavy protests from the Atalanta players and coaches but the decision was allowed to stand, with the VAR not intervening.
This numerical disadvantage saw the hosts withdraw into their shell, with Real Madrid dominating possession, although the Bergamo outfit still threatened to catch Los Blancos out on the counter.
The best chance of the opening 45 minutes came right on the stroke of half-time. Toni Kroos stood over a free-kick and delivered a trademark pristine cross into the area, which Casemiro attacked with a direct header at goal.
The ball, however, went straight to Pierluigi Gollini, who produced an excellent reflex save to keep the scores level.
The second half started with Real Madrid fashioning another good chance in the 47th minute. Luka Modric's shot from the edge of the area was narrowly deflected wide of the bottom post in seemingly slow motion, with everybody rooted to the spot.
The rest of the second half was relatively devoid of goalmouth action, with Real Madrid having just one shot on target until the final 10 minutes.
As time ran out, both managers made some changes in a bid to influence the game.
Luis Muriel went off for Josip Ilisic, while Mariano and youngsters Sergio Arribas and Hugo Duro all came on for Real Madrid.
Despite the changes, chances continued to come at a premium until the deadlock was broken by an unlikely source in the 86th minute.
A corner kick by Toni Kroos was not properly dealt with, allowing Mendy to rifle home a right-footed curler from 25 yards out.
A late surge by Atalanta failed to yield dividends, as Real Madrid held on for a crucial away win.
The return fixture will be played on March 16, and here are five talking points from the game.
#5 Remo Freuler's controversial red card
While the veracity of Freuler's foul on Mendy is not in doubt, questions are bound to be asked over whether it was worth a red card.
In the immediate aftermath of the foul, it was taken for granted that a yellow card would be shown. However, to the astonishment of the players and management staff, a different color was brandished.
Gian Piero Gasperini was beside himself with bemusement, and an assistant behind him seemed confident that the decision would be overturned as he gestured to the VAR with his hand.
However, the center referee's decision stood, and Atalanta had to play out the final 72 minutes of the game one man short.
The rules of the game state that a red card should be shown when a clear goalscoring opportunity has been denied. It cannot be argued that Mendy was cynically denied a goalscoring chance, but the matter of it being clear is open for debate.
A case can be made that Christian Romero beside him was in a good position to cover Mendy as he raced through on goal.
The fact that the VAR did not even deem the decision worthy of a review left a lot to be desired, and Atalanta are well within their right to feel aggrieved.
#4 Unlikely hero Ferland Mendy steps up for Real Madrid
Ferland Mendy has played a key role for Real Madrid in recent weeks, and the 25-year-old once again came to the fore against Atalanta.
Having won the foul that led to the red card for Freuler in the first half, the France international made an even bigger contribution with less than four minutes to go.
The technique shown to curl the ball beyond Gollini's dive from distance was indicative of his talent. The fact that it came from his weaker foot made it more impressive and even drew a rare smile from the normally stoic Zidane on the sideline.
Real Madrid now go into the return leg on the front foot and have their marauding left-back to thank for that.