A first-half Maximilian Baier strike had Hoffenheim on track to break Leverkusen's unbeaten streak, which now stands at 39 matches, just one day after in-demand manager Xabi Alonso pledged his future to the club.
But as they have done regularly this season, Leverkusen fought back late as Andrich levelled the scores in the 88th minute before an injury-time Schick volley sealed another remarkable comeback win.
The victory sends title-bound Leverkusen 13 points clear of Bayern Munich, who face Borussia Dortmund later on Saturday, with seven matches remaining this season. "We kept fighting and kept believing until the end," Andrich said to 'Sky'. "I had no doubt we'd score at least one today, I knew eventually one of our shots had to go in."
The midfielder, who stood alongside his coach as the team celebrated in front of the home fans after the match, said Alonso informed the players on Friday he would stay beyond the season.
"He said he wasn't going anywhere - he said he'd stay here. The timing he chose was very good. Now we can keep pushing and hopefully achieve something great this season."