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 which delighted the fans.
Their lead was cut short, however, when QPR equalized in controversial circumstances just seven minutes later, with Norwich debutant Sebastian 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.
The Canaries had several chances to go back in front, with the best coming from Russell Martin after the right back met Anthony Pilkington's cross, but saw his header loop onto the crossbar. But they could not find the winner against a QPR side which was largely on the back foot for the majority of the game.
It didn't take long for the deadlock to be broken after a delightful team move from the home side. Jonny Howson played the ball into Jackson, who then flicked it on to this strike partner Holt. 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.
Norwich began to enjoy some comfortable possession, with Garrido looking composed at left back, and forming a well-working partnership with Pilkington on the left. However, Norwich soon found itself picking the ball out of the net after a dubious decison from Mark Clattenburg.
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, Clattenburg pointed to the spot, much to Norwich's dismay.
However, when Cisse stepped up, Ruddy did brilliantly to tip his penalty onto the post, but unfortunately for the England international, Zamora was alert to pounce on the rebound, although replays showed the former Fulham striker was in the penalty area when Cisse made contact with the ball.
At the break, Mark Hughes did the wise thing to bring off Cint Hill after enduring a frustrating first half, with Nedum Onuoha replacing him at the heart of the defense, while Hughton opted to keep things as they were, with the East Anglian club unfortunate not to be in front after an impressive first-half showing.
Norwich was happy to keep possession and Jackson again mustered a decent chance for the hosts. The 25-year-old received the ball on the edge of the box before unleashing a left-footed effort, but saw it whistle over the bar to keep the scores level.
The contest was slowly turning into an end-to-end spectacle and QPR was lucky not to concede when Onuoha and Green were caught in two minds attempting to clear a long ball. The goalkeeper was then fortunate not to be sanctioned by Clattenburg when he appeared to handle outside the area.
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.
A magnificent chance then fell to Snodgrass to put Norwich back in front. A great delivery from the left by the excellent Garrido found the unmarked Snodgrass, who glanced his header narrowly over the bar to miss the best chance of the half, with The Canaries hoping they wouldn't be punished for missing their chances.
Minutes later, a frantic phase of play then saw Norwich muster a brilliant chance from the short corner. Pilkington was once again at the heart, with a superb cross from the left finding Martin, who aimed his header back to the far post but was so unlucky to see it bounce of the top of the crossbar.
It was starting to look like one-way traffic as Norwich continued to press on, and Hughes identified that his side was on the back foot, making his final substitution with veteran midfielder Shaun Derry coming on for Malian enforcer Samba Diakite in an attempt to see out the draw.
With three minutes added on, the game slowed as Hoilett went down after a clash of heads, frustrating for Norwich who then lost momentum. Cisse, not for the first time in the match, was then caught offside as QPR looked for an unlikely winner, but it would be the Norwich manager who will be unhappy that his side could not find a goal to steal all three points.