The province looked set for a fourth successive defeat in their European Championship qualifying campaign after substitute Eric-Maxim Choupo-Moting put Germany ahead with a minute remaining.
However Norwood stepped up to the plate and his perfectly-placed effort left goalkeeper Tobias Sippel rooted to the spot.
It was no more than Northern Ireland deserved given the way they had battled and scrapped in difficult conditions.
Port Vale striker James Lawrie almost made the breakthrough a minute into the second half only for his effort to come back off the crossbar.
A minute's silence was held before kick-off as a mark of respect to Robert Enke, following the death of the Hannover goalkeeper this week. A group of Germans fans held up a placard which read: "Robert R.I.P."
Felix Bastians found the net for the visitors after six minutes only to be judged offside before Northern Ireland came close to opening the scoring.
Skipper Craig Cathcart got away from his marker but headed wide from Norwood's free -kick.
Back came Germany and a header by Julian Schieber was collected at the second attempt by goalkeeper Trevor Carson.
It was an open game and Norwood set up Corry Evans in the 26th minute but he fired wide from 20 yards.
Germany stepped up the pace and Thomas Muller got into good positions but saw one effort deflected to safety by Ryan McGivern and another blocked by Lee Hodson.
Schieber should have opened the scoring in the 44th minute but rushed his shot and sent it wide of the post from six yards.
Lawrie then went close before Schieber was again off-target following good work by Sidney Sam.
Norwood sent a good shot from distance into the goalkeeper's arms in the 66th minute and again tested him seven minutes later.
The Old Trafford youngster then picked out Jonny Flynn with a free-kick but he headed over before the dramatic final few minutes.