The feat was achieved after guiding her side to a 3-1 Bundesliga victory over Mainz at the MEWA Arena.
Andrej Ilic gave Union the lead in the 38th minute before Sheraldo Becker equalised for the hosts ten minutes later, before late strikes from Oliver Burke and Josip Juranovic sealed a memorable victory.
“You're happy, you want to win games. That's always the case and so it was today as well,” Eta told DAZN.
“The way it happened was great too, how we managed to pull it off.
“It's been about doing the job as well as possible, getting points, winning games, and that's what we've worked for each day.
“We've invested a lot so it's great that we could get the three points here today, show a good performance, I think, and that's important for me, too.”
The result lifted Union Berlin to 12th in the Bundesliga standings and ended the club’s winless run stretching back to March. Eta took over last month following Steffen Baumgart’s dismissal.