Reading led 2-0 at the interval through a penalty from Hal Robson-Kanu and a close-range effort from Simon Cox.
Bradley Johnson pulled a goal back for the in-form Canaries in controversial circumstances in the second half but Reading held on for their first three-point haul since Clarke replaced Nigel Adkins as boss.
Norwich travelled to Berkshire in rude health, unbeaten in four matches and having scored 14 goals in the process – including the 6-1 home hammering of Millwall on Boxing Day.
In contrast, Reading had won only one of their previous seven matches – 2-1 against Norwich at Carrow Road last month – and Clarke had yet to win in his first two games.
Gary Hooper had scored twice in the rout of Millwall and he could have added to that tally early on, but he blazed over the crossbar after finding time and space at the far post.
Reading replied with a long-distance free-kick from Oliver Norwood that took a deflection and almost deceived Norwich goalkeeper John Ruddy. From Norwood’s resultant corner, Glenn Murray volleyed wildly over.
Norwich’s response was muted and Ruddy had to be alert to keep out a fierce 20-yard drive from Murray. He could do little, though, as Reading took the lead in the 25th minute.
Michael Hector fell under the challenge of Johnson as they jostled to reach a Norwood corner, and referee James Linington pointed to the spot and booked Johnson.
Robson-Kanu sent Ruddy the wrong way with a coolly-taken penalty for Reading’s first goal at home in four matches.
Norwich appeared rattled and fell further behind nine minutes later. Murray crossed from the right and Cox first controlled the ball before planting a crisp shot past Ruddy. It was his eighth goal of the season.
Reading had thrown away a two-goal lead on Friday in their 2-2 draw at Brighton and came under pressure at the start of the second half.
Jonny Howson fired in a cross-shot from the right and Cameron Jerome, Norwich’s most lively forward, was only inches away from connecting with it.
Reading were already playing deeper and relying on the counter-attack, which they twice did to good effect but without the end product.
First, Murray escaped on the right flank but, with Cox available in the middle, he crossed too close to Ruddy. Then, Cox hit his intended centre too strongly from a similar position and another chance went begging.
Norwich reduced the deficit in the 71st minute in bizarre circumstances, when Reading winger Garath McCleary left the pitch injured but Linington restarted play without allowing Reading to replace him.
Johnson took full advantage, with Reading down to 10 men and disorganised, and lashed home a superb 20-yard shot, much to the home players’ fury. Only then were Reading able to replace McCleary with Jamie Mackie.
Although Norwich rallied near the end, Reading held on gamely for Clarke’s first win.