Stindl tapped in after 29 minutes and scored again after second half goals from Fabian Johnson and Raffael, to lift Gladbach to five points in the group and on track for a third place finish that leads to the Europa League, with their last group match against Manchester City next month.
Sevilla, who scored through Vitolo in the 82nd minute with Ever Banega adding a stoppage-time penalty and have now lost their last four group games since beating the Germans in their opener, are in bottom place on three and face Juventus next.
The hosts, who had lost three times this year to Sevilla, including twice in the Europa League, took revenge with their first home win over a Spanish club in 30 years to continue their stellar run under coach Andre Schubert.
Gladbach, who have won seven of their eight matches in the league under Schubert, got off to a better start, with Sevilla keeper Sergio Rico forced to make three saves in the opening minutes.
The visitors, looking to halt a run of three straight defeats, responded with a huge chance by Yevhen Konoplyanka who failed to beat keeper Yann Sommer from three metres out.
Rico was kept busy, however, twice more stopping shots from Stindl but the attacking midfielder was not to be denied, slipping into the box to tap in a Granit Xhaka shot on goal.
The Swiss international almost scored himself early in the second half, unleashing a missile from 20 metres with Rico spectacularly palming the ball wide.
Sevilla upped the tempo and came close twice with Frenchman Kevin Gameiro before Johnson delivered the knockout punch in the 68th with a well-placed curled effort.
Raffael added a third and Vitolo cut the deficit in the 82nd before Stindl responded with his second goal of the evening a minute later in an entertaining finale that included a penalty for Sevilla in stoppage time converted by Ever Banega.
(Reporting by Karolos Grohmann; Editing by Rex Gowar)
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