Striker Marco Reus, who had been doubtful after picking up a muscle injury in the first leg, scored the equaliser in the 72nd minute for Gladbach, who twice hit the woodwork and had won the first leg 1-0 last week.
The five-times Bundesliga champions had won three and drawn one in their last four games of the season under Swiss coach Lucien Favre, climbing out of bottom place to clinch the play-off spot on the last match day.
"This is fantastic," Favre, who took over in February and quickly turned the fate of the club around, told reporters. "This team showed a lot of character. We always believed we can do it."
The hosts were determined to return to top flight football a year after going down and cancelled out Gladbach's first leg advantage when Christoph Dabrowski cut a pass back into the box and Gladbach's Havard Nordtveit tapped it into his own net after 24 minutes.
