© Getty Images
The midfielder controlled the ball and unleashed a shot from the edge of the six-yard box, which nestled into the back of the net.
Despite the positive start, Adelaide were forced to make a change when defender Michael Marrone was stretchered off with an ankle injury within the first five minutes of the half.
Heart were given an opportunity to get themselves back into the match when Elrich gifted the side with a penalty following a poor challenge.
David Williams managed to convert from the spot to draw level, but things began to get heated when Elrich was sent off for a second bookable offence shortly afterwards.
Williams lined up to take the penalty, but Eugene Galekovic managed to save his effort to keep the scoreline level.
However, it wasn't long before Heart took the lead when Mate Dugandzic picked up the ball in the six-yard box and hammered it into the net.
After the break, Heart went on the attack, but Galekovic was able to make another vital stop from Stefan Mauk.
At the other end, Adelaide tried to strike back with a shot from Jeronimo Neumann in the penalty area, but Heart's goalkeeper managed to punch the ball clear.
In the dying minutes of added time Ferreira stepped up for Adelaide to find the back of the net and grab a point for his side.