Romero headed in with 11 minutes to go after Alexander Scholz had put the already-eliminated Danes ahead in the 13th minute in Bergamo.
Atalanta are second in Group D, one point ahead of third-placed Ajax, who lost 1-0 at Liverpool, who wrapped up top spot.
Atalanta and Ajax will to head-to-head in Amsterdam on December 9 for a place in the knock-out stage.
Gian Piero Gasperini's side stunned Liverpool at Anfield last week, and had eased past the Danes 4-0 earlier in the campaign.
But they have not won at home this season in the Champions League, with their last success at the Gewiss Stadium coming in Serie A on October 4.
Atalanta were wasteful in the first half, lacking precision in front of goal despite having 11 attempts before the break.
The hosts had three chances before Midtjylland captain Scholz opened the scoring, with Luis Muriel sending Duvan Zapata in on goal, only for his fellow Colombian to fire over.
The pair combined to tee up Hans Hateboer but the Dutch wing-back fired straight at visiting goalkeeper Jesper Hansen.
Captain Papu Gomez helped Zapata get in behind again, but his effort was easily saved by Hansen.
Midtjylland grabbed the lead, though, as Sory Kaba chested the ball down for Scholz to blast a fierce drive past a helpless Marco Sportiello.
Matteo Pessina struck a shot wide from a tight angle after half an hour, with Zapata and Muriel efforts lacking the power to beat Hansen.
Josip Ilicic replaced Gomez at half-time, before Gasperini made a triple change on 68 minutes with Amad Diallo replacing Muriel, and Marten de Roon and Rafael Toloi also coming off the bench.
But Robin Gosens and Zapata both blasted over with only the goalkeeper to beat, while 18-year-old Ivorian winger Diallo, who is set to join Manchester United in January, also missed two chances.
The pressure finally paid off, with Romero rising highest to meet a Hateboer cross, heading the ball past Hansen and into the corner.
The Argentine also wasted the opportunity for a last-gasp winner, heading over the bar just before the final whistle.