Goals from Kenny McLean and Josh Sargent were not enough to take away all three points against Queens Park Rangers in a 2-2 draw at Loftus Road on Saturday afternoon.
McLean found an equaliser early in the second half after the hosts had gone ahead and the City number nine put the Canaries ahead after an hour.
They were unable to hold onto the lead as substitute Michael Frey made it 2-2 after 77 minutes.
There were just two changes to David Wagner's starting 11 following the 2-1 win against Coventry City, with Ashley Barnes coming in off the bench for Marcelino Núñez and the injured Shane Duffy making way for Grant Hanley.
QPR came into the game having picked up seven points from a possible nine in their last three games, whilst Norwich were looking for back-to-back league wins for the first time since mid-January.
Chris Willock was unfortunate not to find the end of Ilias Chair's cross into the box in the opening minutes for the first convincing chance of the match.
City's Borja Sainz had a go at goal after a corner fell to him on the edge of the area, but the Spaniard couldn't lower his effort enough to find the target in the opening 10 minutes.
A strike from distance by Joe Hodge later on narrowly dragged wide of Norwich's left post.
Angus Gunn was first called into action just before 20 minutes, reacting quickly to Willock's close-range poke towards goal.
Sainz was inches away from the target with his second attempt after QPR allowed him room to shoot from the edge of the box.
It was the Rs who found the back of the net first though, as Gunn initially did well to parry the ball away from goal but Jack Colback latched onto the rebound and buried his effort to put the hosts ahead inside half an hour.
Norwich managed spells of pressing for the remainder of the half but were unable to trouble Asmir Begović in goal.
The second half opened lively and saw a quick response from Norwich to get things back on level terms.
Gabriel Sara took a corner in front of the travelling fans and found McLean waiting in the box, who slotted home to make it 1-1 on 48 minutes.
Hodge had an effort trickle past Gunn and the wrong side of the post to stop the hosts going in front again shortly after.
The game was then turned on its head shortly after Jonathan Rowe made his way onto the pitch on the hour mark.
City's top scorer slotted a ball to Jack Stacey on the right, who picked out Sargent towering above his marker in the box to head home and put Norwich in front.
A quick succession of chances then fell to the hosts, but none could find the target following Norwich's second.
With 15 minutes to go on the clock, QPR's pressing was eventually rewarded when substitute Frey found an equaliser on the end of Lucas Anderson's cross.
Barnes looked to be on target in the box shortly after, but his shot was defected away for a corner.
Both sides had the chance to put the game to bed in the dying minutes, but neither could finish an opportunity.
Norwich City are back in Championship action on Tuesday, February 13, hosting Watford at home.
QPR: Begovic; Cannon, Cook, Clarke-Salter Paal; Hayden (Dykes 85), Colback, Willock (Smyth 66), Chair (Dixon-Bonner 90), Hodge (Andersen 66); Armstrong (Frey 66)
Unused subs: Archer, Dunne, Fox, Larkeche
Goals: Colback (27), Frey (77)
Bookings: Chair (80), Clarke-Salter (87)
Norwich City: Gunn; Stacey (Sørensen 69), Hanley, Gibson, Giannoulis (McCallum 85); McLean, Sara, Fassnacht (Rowe 58), Sainz (Hernández 85); Sargent (Núñez 69), Barnes
Unused subs: Long, Batth, Gibbs, Hooijdonk
Goals: McLean (48), Sargent (62)
Bookings: Gibson (25), McLean (52), Hanley (76), McCallum (90+7)
HT: 1-0
FT: 2-2
Referee: Ben Toner
Venue: MATRADE Loftus Road
Attendance: 17,831