With the match surprisingly lifeless and heading towards a scoreless draw inside the final 20 minutes, Frankfurt's Fares Chaibi shot over the bar with an empty goal beckoning. Two minutes later, Gittens cut back in from the left flank and blasted a shot in off the crossbar.
Gittens, who changed his name from Bynoe-Gittens in the summer, had come off the bench just 14 minutes earlier. In the third minute of added time and with Frankfurt pushing for an equaliser, Gittens collected the ball inside his own half and powered up the pitch, firing in his second to seal the match.
"It's a crazy feeling to score not one but two," Gittens told Sky. "First game of the season, it's very important. That was very good today."
The result means new Dortmund coach Nuri Sahin, who replaced Edin Terzic in the, can celebrate his Bundesliga debut with a victory.