Ryan Sessegnon scored a late goal to snatch win and stretch the hosts' winless run to six games in all competitions.
But they struggled to build on the opener and Hoffenheim deservedly equalised through Andrej Kramaric in the 75th before Thuram was sent off after VAR upgraded his yellow card to a red.
The visitors made their one-man advantage count when Sessegnon, on loan from Tottenham Hotspur, pounced to claim all three points four minutes from time as Hoffenheim climbed to 11th with 15 points, while Gladbach stay eighth on 18.
"It's just a no-go," Gladbach manager Marco Rose said of Thuram's red card. "It's beyond anything.
"He can only apologise. We can only apologise for it. He also hurt his team. But that's not the point right now. It does not belong on any football pitch. He is a good lad and he will reflect it."
Information from ESPN's Germany correspondent Stephan Uersfeld was used in this report