The Potters enjoyed the better of the first half but were unable to convert the opportunities that came their way, with John Ruddy making saves to deny Jon Walters, Dean Whitehead and Peter Crouch.
Tony Pulis' men continued to press after the break and Etherington struck in the 72nd minute after collecting the ball from substitute Cameron Jerome, who had flicked on a throw-in it appeared the hosts had been fortunate to be awarded.
The result means Stoke continue their recent recovery from a four-match losing streak in the Premier League, following up last week's 2-0 win against Swansea.
The Staffordshire outfit are up to eight in the table, while Norwich drop to 10th.
The only change to the Potters starting line-up from the Swansea game saw defender Robert Huth return after serving a three-match suspension, replacing Matthew Upson.
Norwich's first XI showed three adjustments from their 2-1 defeat to Manchester United, manager Paul Lambert bringing in midfielder Jonny Howson for his Canaries debut, as well as Elliott Bennett and Russell Martin, with Simeon Jackson, David Fox and Adam Drury the men making way.
Walters made the game's first attempt on goal in the ninth minute, getting the better of Kyle Naughton and unleashing a fierce strike which goalkeeper Ruddy initially parried before gathering.
Six minutes later, Huth came forward to get on the end of Ryan Shotton's cross but the German could not direct his header on target.
Referee Michael Oliver waved for play to continue when Shotton went down in the area under the attentions of Naughton, and then penalised Crouch for committing a foul as the forward jumped to head the ball at Ruddy.
Howson picked up a booking for a challenge on Glenn Whelan, before Walters slipped in Whitehead, who could not get sufficient power on his effort to trouble Ruddy.
Stoke were forced to make a substitution in the 25th minute, with Andy Wilkinson having to come off for Jermaine Pennant, and Huth then swung a wild attempt into the stands.
Norwich had offered little going forward, but called Asmir Begovic into action on the half-hour mark when Grant Holt met a free-kick with a header at the far post.
Holt hacked a shot wide from outside the box five minutes later, but it was the Potters who went close just before the break, Crouch having a header blocked by Bradley Johnson and then a shot kept out by Ruddy.
Lambert changed things around at half-time, substituting Anthony Pilkington for Jackson.
Crouch tried to connect with an Etherington cross but was beaten to the ball by Naughton, with Ruddy punching away the resulting corner, and at the other end a tame shot from Bennett rolled through to Begovic.
Crouch flicked a header wide before Holt won a free-kick in a useful position which was taken by Andrew Surman and caught by Begovic.
Pulis refreshed his attack by replacing Walters and Crouch with Jerome and Kenwyne Jones, and within three minutes the hosts finally broke Norwich's resistance.
From a throw-in - which replays suggested perhaps should have been given to the Canaries - Jerome headed the ball to Etherington, who touched it past Elliott Ward before firing beyond Ruddy.
The lively Etherington then delivered a cross which looped wide off Jones' head.
Martin got in the way of a shot by Jerome in the final 10 minutes, but Stoke had done enough.