Wade Small struck 14 minutes from time to earn Wednesday a victory which moves them off the bottom of the table. Small drilled home a low shot from Frankie Simek's cross to cap a spell of pressure from the visitors.
The strike secured Wednesday's first away win since April, while fellow strugglers Norwich slipped to their fourth consecutive defeat.
Norwich almost drew level late on but substitute David Strahava could not connect with Jon Otsemobor's cross.
Norwich manager Peter Grant on being booed off: "I don't like losing matches either, and I can fully understand the fans' frustration. "We deserved that reaction because we have lost another match at home, another one we shouldn't be losing.
"I want this place to be rocking, but that's not going to happen with performances like that, I know."
Sheffield Wednesday manager Brian Laws on back-to-back wins: "I don't like being associated with a run of six straight defeats, the worst in the club's history. I'm not proud of that at all. "But if you come through something like this, you tend to be a better man at the end of it.
"It was vital that when we created a good opportunity we took it, and fortunately that was the case. We showed a bit of quality at times, and I thought we deserved the three points."
Norwich: Marshall, Otsemobor, Doherty, Murray, Drury, Jarvis, Spillane (Croft 62), Lappin, Huckerby, Brown (Strihavka 74), Cureton.
Subs not used: Gilks, Russell, Martin. Booked: Spillane, Cureton. Sheff Wed: Grant, Simek, Wood, Michael Johnson, Spurr (Hinds 76), Watson (Jermaine Johnson 52), Kavanagh, Whelan, Small, Jeffers (Tudgay 33), Burton.
Subs not used: Burch, Sodje. Booked: Kavanagh, Whelan. Goal: Small 76 Attendance: 23,293
Referee: Mike Russell (Hertfordshire).
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