Danny Rohl's team spent long periods playing catch-up, as they fell behind early when Ebou Adams scored to put the Rams in front.
But after Barry Bannan's memorable finish had dragged Wednesday level, substitute Lowe pounced in the fourth minute of stoppage time from close range to snatch the points.
For the hosts, manager Paul Warne, who had seen Jerry Yates spurn a glorious chance shortly before Bannan levelled, it was a case of what might have been.
Derby started brightly, with Owls skipper Bannan conceding possession in midfield and allowing Nathaniel Mendez-Laing to whip a dangerous cross into the box.
TrendingAdams headed clear a thunderous effort from Marvin Johnson but recovered quickly to fire Derby into a ninth-minute lead. Marcus Harness beat his marker and produced a pinpoint centre which Adams powered home.
The Rams spurned an opportunity to double their advantage when Craig Forsyth blazed a first-time shot over the crossbar before Wednesday began to find their rhythm.
A period of pressure towards the end of the half saw goalkeeper Jacob Widell Zetterstrom finally called into action to deal with a series of high balls into his area.
Rohl introduced Liam Palmer and Josh Windass at the break and the latter's presence created the space for Anthony Musaba to try his luck after meeting Bannan's free-kick but the Dutchman's shot flew high and wide.
Yates should have punished that miss but could not beat keeper James Beadle from close range despite being left unmarked.
Only the width of the crossbar prevented Warne's team from putting the game to bed when Yates connected with Ben Osborn's corner.
That was the cue for Bannan to punish Derby's profligacy, curling a wonderful 64th-minute strike past Zetterstrom when the hosts failed to clear their lines.
Then, with almost the final kick of the game, Lowe fired home to shock the Rams.
Derby's Paul Warne:
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Sheffield Wednesday's Danny Rohl:
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