The 24-year-old came on for Ludmila da Silva in the 72nd minute to make her debut for the Spanish champions - few days after completing her loan switch from US-based side Washington Spirit.
After defeating Sporting de Huelva, Angel Villa Carrasco's side made a poor start as Andressa Alves's 27th minute gave the visitors the first half lead.
Kenti Robles restored pride for the home team as she netted in the 63rd minute to snatch a point for Atletico before Barca's Victoria Losada got sent off 10 minutes to full time.
Villa's ladies latest draw leaves them in the second position with 19 points - same as leaders Barcelona who holds an 11 goals advantage after seven games.
Ordega will be hoping for her starting debut against Madrid in next league encounter at the Centro Deportivo Municipal Luis Aragonés on November 5.