It was their first league defeat of the season and snapped Leipzig's nine-game unbeaten run away from home.
The hosts should have scored again but Plea rattled the bar with a powerful shot. Leipzig, who were demolished 5-0 by Manchester United in the Champions League in midweek, were toothless apart from two first half Yussuf Poulsen efforts.
"It kind of felt like a draw," said Leipzig coach Julian Nagelsmann. "Our pressure over 90 minutes was just not enough to speak of an unfortunate defeat. But it was also not a hugely deserved defeat."
Wolf spent a hapless season at Leipzig after joining from sister club Salzburg and, with only a handful of appearances last term, made more headlines off the pitch with social media posts of luxury watches, expensive restaurants and private jets.
"A weight has been lifted off my shoulders," Wolf said. "I had been waiting for such a moment for a year and a half. Such a game gives you self-confidence. I seem myself as a Gladbach player and hope to be here for longer than just a year."