A 46th minute strike from the Scottish midfielder was enough for Tony Pulis' men against the Canaries, taking the Potters to the 40 point mark which should see them survive
In a largely nervy and unspectacular affair the Potters were able to secure their second consecutive win for the first time since December, which moves them to the 40 point mark.
Stoke pressed forward immediately at the start of the second half, and Peter Crouch's long range pass found Adam who coolly slotted the ball past Mark Bunn in the Norwich goal.
Tony Pulis had the benefit of naming an unchanged team from the side that recording only their second victory of 2013 against QPR last weekend.
In the opposite dugout, Chris Hughton made three changes from the side that all but condemned Reading to relegation in their 2-1 victory last week. Russell Bennett replaced Michael Turner, Javier Garrido made way for Steven Whittaker and Alex Tettey started ahead of last week’s goal scoring hero Elliott Bennett.
The first half passed by with very little action, as to be expected from two teams who have collectively amassed the fewest Premier League victories in 2013.
The first real chance of the game came after 20 minutes when Cameron Jerome's strike from a corner hit Steven N'Zonzi, who appeared to move his arm towards the goal-bound strike.
Minutes later N'Zonzi was at the centre of the action yet again, though he will know he was fortunate to stay on the field.
The Stoke midfielder was dispossessed by Kei Kamara and the 24-year-old Frenchman scythed down Kamara with his feet off the floor. Referee Anthony Taylor leniently opted to show N'Zonzi a yellow, though it perhaps should have been a red.
In the 42nd minute, Stoke fans respectfully held a minute's applause in memory of former player Paul Ware who recently died at the age of 42, before Taylor brought the first half to a close.
It took just one second-half minute for the game to liven up. Peter Crouch flicked a long ball into the path of Adam, who controlled the pass well before slotting the ball past Bunn in the Norwich goal to give the hosts the lead.
With Stoke dominating the majority of the possession, there were little chances created with Pulis' men seemingly satisfied with a one goal lead.
As the second half wore on, Stoke dropped deeper although still in control with Norwich creating very few clear cut opportunities.
A long throw from Russell Bennett almost caused the Potters a problem in the final minute of stoppage time, but Kamara's header was wild and Stoke held on for a vital victory.
Defeat for Norwich means the Canaries have not won in eight games and the Britannia Stadium side are six points clear of the relegation zone.