The Canaries found themselves 2-1 to the good at the break after strikes by Teemu Pukki and Todd Cantwell sandwiched a retaken Pierre-Emerick Aubameyang penalty, only for the Gabon striker to equalise in the second half as Bernd Leno spared the blushes of the visitors with a number of outstanding saves.
Arsenal end the weekend in eighth after six Premier League games without a victory, whilst Norwich continue to find themselves stranded in the relegation zone despite manufacturing four points from their last two matches.
Pukki back amongst the goals
Whilst the Canaries made just one change from last weekend as Ibrahim Amadou returned to midfield in replace of the absent Alex Tettey, Arsenal made a quartet of adjustments and started the game with four in defence - Ljungberg setting out his vision early during the post-Unai Emery era after the Spaniard chopped and changed from four to three at the back and vice-versa, no less than 23 times last season.
The visitors started with a point to prove and almost opened the scoring within minutes of kick-off. Shkdoran Mustafi connected with a corner as Tim Krul misjudged a charge off the line, only for Onel Hernandez to clear from underneath his own crossbar.
But the home side were ahead within 21 minutes as Teemu Pukki ended a goal drought that had dragged on longer than Arsenal's winless run.
The impressive Kenny McLean fed the striker from midfield before Pukki turned and was granted freedom to press forward in front of David Luiz. The Finn cut inside before unleashing a deflected effort off Mustafi and into the bottom corner.
Penalty drama as Norwich implode
But, within minutes, Arsenal were level after a series of errors from the hosts.
As he grappled with Luiz from a free-kick, Christoph Zimmermann raised his hand and then turned his back before deflecting the ball with his fingers to grant the visitors a penalty.
The initial effort from Aubameyang was saved by Krul down to his right but VAR spotted no less than four yellow shirts encroaching and the penalty was retaken.
This time, there was no mistake from the Arsenal captain, keeping the armband despite the return of Granit Xhaka, firing to Krul's right again as the Dutchman dived the wrong way.
Cantwell at the double
After a period of loose passing from both sides, Norwich netted a second just moments before the break.
Again, it was McLean driving forward from midfield who created the opportunity, this time releasing Hernandez down the left. The Cuban laid the ball to Cantwell who, like Pukki earlier in the half, was allowed yards of space by the Arsenal defence.
The midfielder simply picked his spot and placed Norwich into a half-time lead with his second goal in as many matches.
Home side fail to deal with another set-piece
In an open start to the second half, it was clear there would be at least another goal with both sides looking nervy at the back.
With 57 minutes on the clock, Mesut Ozil's whipped corner enticed the Norwich defence to shuffle across, leaving Aubameyang free at the back post after a deflected clearance landed at the Gabon international's feet before smashing into the roof of the net.
Shortly after the equaliser, Amadou hunted the ball down in midfield before Matteo Guendouzi failed to clear the increasing danger. Pukki played McLean through but his strike was brilliantly saved by the outstretched Leno to turn the ball against the post.
Leno saves the visitors
The pressure continued as Norwich looked the most likely to capture all three points.
Pukki was kept out by another strong save before Leno palmed a dangerous McLean free-kick round the post.
Cantwell was then inches away from netting another home goal but his side-foot effort flew just past the woodwork with Leno stranded on this occasion.
Neither side looked happy to settle for a point as wave after wave of attack at either end was sustained. Lucas Torreira and Amadou made solid blocks in front of their respective goals, whilst Krul kept out Aubameyang from close range.
As the full-time whistle blew, Ljungberg cut a figure of frustration but he may feel lucky to have escaped with a point.
McLean the driving force
Whilst the likes of Teemu Pukki and Todd Cantwell have refound their form in front of goal, Kenny McLean has made a huge difference in the middle of the park.
The Scotsman was the driving force in the victory against Everton with five key passes before following up that performance by starting off the moves for both Norwich goals in another crucial fixture.