Qualls has been a pitcher in the dugout who has been looked at as the "lefty specialist" without having to be a lefty pitcher. His movement on his sliders and cut fastball made him an effective pitcher against left-handed batters. But the reality is that he hasn't been as effective this year in that role as he has in the past. With the emergence of Sipp as a reliable 7th inning pitcher, the reliance of Harris as the 8th inning pitcher, and the failure of Neshek in any of the roles Sipp and Harris have undertaken, the use of Qualls as primarily a one batter reliever made him expendable in a way. Also, you saw perfectly the pattern Hinch planned for when he reformatted his pen for the playoff, especially against the lefty hitting Royals team.
He used Sipp in the 7th and left him in there to pitch the entire inning, a change in his role. He used Harris in the 8th and when trouble came a'knockin, he quickly summoned his now lefty specialist... Oliver Perez. In years past, that would have been Qualls. Neshek warming in the 7th tells you his new role... a righty specialist that will be called on to pitch to one guy only in case Sipp needs the support.
So Sipp/Neshek or Sipp/Qualls. Somehow, Hinch has decided that Sipp/Neshek works best because right now, the stuff Neshek has could help him get a key out in the 7th if needed when it's a situation that calls for a righty specialist.