Denis outjumped his compatriot Walter Samuel in the 25th minute and directed a powerful header into the top corner from a Maxi Moralez cross for his fifth goal of the season after Ricardo Alvarez had given Inter a 16th minute lead.
Fourth-placed Inter, who are eight points behind leaders AS Roma with 19 points from 10 matches having played one game more, have won only one of their last five.
Atalanta, unbeaten at home by Inter in the last five years and who completed a double over their opponents last season, are eighth on 13 points after their first draw of the season.
The burly 32-year-old Denis, at his 10th club including his fourth in Italy, has blossomed late in his career after scoring 15 Serie A goals last season and 16 before that.
However, his performances have made little impact back home and he made the last of his five Argentina appearances under Diego Maradona in 2008.
Fellow Argentine Alvarez, another player who has struggled to get a look-in with the national team, opened the scoring from close range after Rodrigo Palacio knocked the ball down to him.
Argentine players were in the thick of the action after the break as substitute Mauro Icardi hit the post for Inter while goalkeeper Juan Pablo Carrizo saved the visitors by blocking a close-range Mario Yepes shot with his legs.
Carrizo had replaced injured Inter goalkeeper Samir Handanovic at halftime.
Inter's Alvarez came close to a winner with the last kick of the match when his long-range effort screamed narrowly wide.
- Sports & Recreation
- Walter Samuel