Becoming only the sixth player to reach a half-century of goals across all competitions under his compatriot also ended the striker's drought stretching back to a Champions League clash against Arsenal on April 29.
Any hopes the visitors had of pushing for a winner were dashed in the 64th minute when Morten Hjulmand was sent off for a reckless challenge on impressive midfielder Angelo Stiller, though Stuttgart defender Jeff Chabot headed Maximilian Mittelstadt's corner wide late on.
Addressing his forward's equaliser and the red card that forced his side to defend for the final 26 minutes, Simeone told Movistar: "I was sure the goal was going to come. We got the 1-1, and we couldn't keep the game where we wanted because of the sending off, which affected us.
"The sending off was fair. I always tell the boys: whenever you leave the floor, you're close to a red card."