The La Liga leaders are yet to concede a goal in the competition, following identical 1-0 wins over PSV Eindhoven and Bayern Munich, and entered the game on the back of a 7-1 victory over Granada on Saturday.
The Russian’s defence held firm in the opening half before in-form Yannick Carrasco – who scored a hat-trick at the weekend – broke the deadlock with a close range volley from Juanfran’s cross to make it three wins from three.
Carrasco now boasts five goals from his last four games for Atletico after having failed to score in his first seven outings of the season.
The Spaniard’s laboured win handed Rostov their first home defeat in 26 games.
Atletico were hot favourites and should have taken the lead after just 90 seconds. Soslan Dzhanaev could only weakly parry Carrasco’s free kick straight into the path of Angel Correa who screwed his shot wide.
Dzhanaev made up for his error by saving well from Carrasco and midway through the half Correra wastefully blazed over from close range.
The La Liga side continued to dominate in the second half but they had to wait until just before the hour mark until they had a decent effort on goal as Fernando Torres’s header went inches over the bar.
The breakthrough came soon afterwards as Rostov failed to cut out Juanfran’s cross and the ball dropped invitingly for Carrasco, who drilled a fierce left-foot shot past Dzhanaev.
Atletico’s star attacking midfielder Antoine Griezmann started the game slowly but played an increasingly valuable role in the second half and could have scored Atletico’s second in the 83rd, but Dzhanaev made the save.
Defensively minded Rostov has one point from three games in its Champions League debut campaign and rarely threatened to score against Atletico, barring a couple of late efforts easily dealt with by goalkeeper Jan Oblak.
In the group’s other game, Bayern Munich crushed Dutch side PSV Eindhoven 4-1 to bounce back after three games without a win in all competitions and take a big step towards the last 16.
What had started as a walk in the park with Bayern riding roughshod over the Dutch with goals from Thomas Mueller and Joshua Kimmich turned into a nervous affair after PSV pulled a goal back through Luciano Narsingh before half time.
The German champions, however, second in the group on six points, kept their cool and Robert Lewandowski headed in the third goal on the hour.