The Canaries were dominant in spells and had many chances to secure victory at home but Mark Hughes' men held on as both sides secured their first point of the season
Simeon Jackson gave the hosts the lead just after 10 minutes, meeting a cross from Robert Snodgrass with a header to hand the Canaries an early lead after an excellent team move.
QPR equalised in controversial circumstances just seven minutes later, Sebastien Bassong bringing down Djibril Cisse in the penalty area despite replays showing minimal contact. Keeper John Ruddy then saved Cisse's weak effort, but Bobby Zamora knocked in the rebound, despite appearing to encroach into the area before the spot-kick was taken.
After being handed 5-0 drubbings last weekend, both managers wanted a change in fortune, with Norwich manager Chris Hughton ringing in the changes as he gave debuts to Bassong and Javier Garrido, while Mark Hughes opted to keep faith with the team who were demolished by Swansea a week ago, with new signing Jose Bosingwa on the bench.
It did not take long for the deadlock to be broken after a delightful team move from the home side. A neat exchange between Bradley Johnson and Anthony Pilkington saw the former Huddersfield winger cross to the far post, with Jackson there to head home.
Soon after, Junior Hoilett ran at Snodgrass down the left, twisting and turning before cutting inside and rolling a pass into Cisse. The Frenchman didn't seem to have the ball under control and went down under pressure from Bassong, and despite not appealing for a penalty, Mark Clattenburg pointed to the spot.
However, when Cisse stepped up, Ruddy did brilliantly to tip his penalty onto the post, but Zamora was alert to pounce on the rebound, although replays showed the former Fulham striker was in the penalty area when Cisse took the spot-kick.
The home side were well on top despite the goal, Snodgrass and Howson combining well in midfield, before the Scotland international cut in from the right-hand side to hit a well-placed effort from 25 yards, but Rob Green was equal to it as half-time approached.
Mark Hughes hauled the booked Clint Hill off at the break, bringing Nedum Onuoha on in his place as the Hoops looked for a first away win under the Welshman.
The Canaries continued to threaten in the second period, Jackson buzzing around up front, but QPR looked dangerous on the break, Cisse just unable to latch onto Zamora's through ball.
Bassong then had a golden chance to put Norwich in front again. Snodgrass won a free-kick on the right-hand side after being tugged by Ji-Sung Park, and the Scot's whipped delivery found the Cameroonian, but somehow headed wide from 10 yards out.
The Hoops were on the ropes and a great delivery from the left by Garrido found Snodgrass unmarked, but the former Leeds man headed over from close range.
The game was Norwich's to win, Pilkington hit a superb cross from the left finding Chris Martin, who aimed his header back to the far post but was so unlucky to see it bounce of the top of the crossbar.
The Hoops held out and the game ended in a stalemate to give both sides their first point of the season.