The host side was already a goal to the good at the Riazor when Pedraza slid in hard and left Bergantinos with cuts to his face.
Depor's captain had to be taken from the field on a stretcher and was taken to hospital for treatment, while Pedraza was shown a straight red card.
That dismissal arrived in the 41st minute, shortly after Depor had opened the scoring via Fede Cartabia's superb free-kick, whipped into the top-right corner from an acute angle.
Quique added a potentially crucial second 11 minutes from time, hooking in Carlos Fernandez's header back across goal.
The second leg takes place at Mallorca on Sunday as Depor seek an immediate return to LaLiga, having suffered relegation from the top fight in 2017-2018.