Defeat at Southampton last time out had seen the pressure on home boss Chris Hughton increase, but City were ruthless during a one-sided first half at Carrow Road that set them on the way to victory.
Robert Snodgrass broke the deadlock in the 20th minute with a well-placed finish, before Alex Tettey doubled the lead with a superb 30-yard volley.
The visitors improved after the break and Wes Brown went close with 50 minutes gone, but any chance of a late comeback ended with Marcos Alonso's stoppage-time sending off for a second booking.
Victory sees Norwich put seven points between themselves and the relegation zone, while Sunderland stay in deep trouble in the bottom three.
Hughton spoke in the build-up of his pride at becoming Norwich's longest-serving Premier League manager, although he was keen to stress that his focus remains on helping to ensure their top-flight status for another year.
They made an encouraging start in that bid, the hosts unlucky not to earn a penalty in the seventh minute when Sebastien Bassong appeared to be brought down by Brown.
After 20 excellent minutes, Norwich took the lead through Snodgrass, as the Scotland winger arrived late into the penalty area and coolly slotted past Vito Mannone following Johan Elmander's cut-back.
Norwich nearly made it 2-0 six minutes later, but Ricky van Wolfswinkel failed to tap in Wes Hoolahan's low cross.
Their second eventually arrived in the 33rd minute, and it came in spectacular fashion.
Hoolahan saw his initial cross headed away by John O'Shea, but Tettey latched on to the loose ball before sending a stunning volley into the top corner from 30 yards.
Both goalkeepers played key roles early in the second period, as Mannone tipped a Van Wolfswinkel header over the crossbar, before John Ruddy denied Brown at the other end from point-blank range.
Sunderland showed renewed focus in the second half and had much more of the ball, but Norwich still looked more threatening on the counter-attack, with Snodgrass almost getting his second of the match before Brown made a crucial block.
Norwich seemed set to regain control going into the final 20 minutes and Hoolahan tested Mannone once more after a clever interchange with Gary Hooper, but the Italian goalkeeper saved down to his left.
Things got worse for Sunderland before the end too, as Alonso was shown a second yellow card for a cynical foul on Snodgrass in stoppage time, compounding a miserable day for the visitors.
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