Just before half-time, Dortmund captain Marco Reus swung in a free-kick from just outside the box to Brandt, who looked to be trying to get out of the way, but the ball skimmed off his back and into the net.
Brandt, who was named Bundesliga player of the month on Thursday, has now scored in five consecutive matches for Dortmund, who are on a nine-match winning streak.
He said his side "pushed our luck a bit" but declared the victory was a "strong snapshot" of where the team is right now.
"In the past we've often lost games like that," he said.
After the break, Dortmund midfielder Emre Can's clumsy challenge on Hoffenheim midfielder Kevin Akpoguma inside the box survived a VAR review, despite the former Liverpool player clearly clipping his opponent's heel.
Dortmund winger Marius Wolf looked to have doubled his side's lead after 57 minutes when he struck a lifting ball past 'keeper Oliver Baumann, but the goal was ruled out for a foul at the other end of the pitch in the build up.
Hoffenheim's Fisnik Asllani had a late chance to equalise when Angelino found him unmarked a metre from Dortmund's goal, but the striker headed just wide.
Bayern Munich and Union Berlin, both three points behind Dortmund, will have a chance to cut the lead when they meet on Sunday in the Bavarian capital.
'Pain-free' Werner
Elsewhere, RB Leipzig climbed into the top four with a 2-1 home win over Eintracht Frankfurt.
Leipzig took the lead after just six minutes, with Timo Werner chipping the ball in despite losing his balance on the edge of the box.
Emil Forsberg, who assisted Werner's effort, doubled Leipzig's lead in the 40th minute.
Frankfurt's Djibril Sow scored a 61st minute screamer to give the visitors hope, but Leipzig held on to leapfrog Freiburg into fourth.
Werner said his team "deserved to win" after "a really strong first half" and revealed only now has he fully recovered from the syndesmosis injury which kept him out of the World Cup.
"I'm pain-free after my injury. I am no longer restricted, which makes a big difference."
Wolfsburg won their first game in six matches with a 2-0 victory at Cologne, thanks to a goal from Yannick Gerhardt and a penalty from captain Max Arnold.
Hertha Berlin beat Augsburg 2-0 to leap three places up the table and out of the relegation zone.
Hertha's Marco Richter and Dodi Lukebakio scored two second-half goals at a snow-covered Olympic Stadium for just their second victory in seven matches in 2023.
The Bundesliga's leading scorer this season, Werder Bremen's Niclas Fuellkrug, scored his 14th goal of the campaign alongside strikes from Niklas Schmidt and Marvin Ducksch in a 3-0 home win over Bochum.
In Saturday's late game, bottom club Schalke host Stuttgart.
