Winger Hazard appeared off the bench for the final 20 minutes of the UEFA Champions League clash in Germany after recovering from a muscle injury in his right leg sustained at the end of September.
That issue was the latest in a series of setbacks for the Belgium international, who has struggled since signing from Chelsea for €100million in June 2019.
Hazard, who had 16 goals in 37 games in his final Premier League season, scored just once in 16 LaLiga matches last term, missing four big chances.
The former Lille star's creativity was also greatly reduced, assisting only three goals in the league for Madrid compared to 15 the previous campaign with Chelsea.
He laid on 1.7 chances per 90 minutes across his first season in Spain, down from 3.0 in the prior term.
But Hazard was simply happy to be back on the pitch against Gladbach, saying: "I am here to play football.
"After two or three months without playing, I am very happy. All I want is to play."
Madrid was 2-0 down when Hazard was introduced, before strikes from Karim Benzema and Casemiro rescued a late draw.
The substitute was not involved in either goal, failing to create a chance while missing a clear opportunity of his own, but was delighted to be involved in the dramatic comeback.
"I think we have shown great character," Hazard said. "We were losing 2-0 and, in the final moments, we could even have scored more.
"I could have scored, but I missed. We did not get three points, but the result tastes like victory."