Rangers went into the clash in northern Germany with key strikers missing.
With Daniel Cousin's fractured jaw ruling him out, Jean-Claude Darcheville absent with an Achilles injury and Lee McCulloch on the bench, Novo came into the side to play as the lone striker.
Holding midfielders Brahim Hemdani and Christian Dailly were handed the task of stopping Bremen midfield orchestrator Diego, who started despite a recent dressing room bust-up with striker Aaron Hunt.
Bremen had not beaten Scottish opposition at home in Europe, and coach Thomas Schaaf kept faith in goalkeeper Wiese despite conceding eight goals in the last two matches.
Werder, as expected, started in vigorous fashion, constantly pushing the Scots back, and in the 14th minute Swedish dangerman Rosenberg powered a right-foot shot that McGregor palmed away.
Rangers' Steve Davis (right) is challenged by Sebastian Boenisch
An exquisite pass from Diego split the Rangers defence a few minutes later, but Tim Borowski's instinctive volley went wide.
Bremen were examining Rangers' rearguard intensely, and Jensen blasted a loose ball goalward in the penalty area only for an alert McGregor to frustrate him.
Wiese turned away an angled Novo effort on the half-hour in a rare Rangers raid, with Bremen still unable to make capital from their dominance.
Rosenberg swiped at a Per Mertesacker header in the box to squander another chance.
Rangers, however, made it to the interval with their first-leg lead intact.
The Germans resumed their pressing game after the break and McGregor twice denied Jensen as the embattled Light Blues held on.
But Rangers' resistance was eventually pierced with a sublime Diego drive that hauled Schaff's men back into the tie.
The Brazilian chested down Kirk Broadfoot's headed clearance before crashing a shot past McGregor low into the left-hand corner of the net from 20 yards out.
It was a deserved lifeline for the hosts who were more than atoning for their slack performance at Ibrox.
Rangers simply could not find any rhythm, with Novo an increasingly marginal figure up front.
David Weir and Carlos Cuellar in defence typified the visitors' spirit as Bremen grew increasingly anxious.
And when McGregor sensationally turned Sanogo's effort onto the bar from close range with just minutes left, it pointed the way to a distinguished victory in Europe for Walter Smith's men.
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