A James Horsfield penalty after an hour opened the scoring for the Blues, but a spectacular free kick from the opposition captain levelled things up 15 minutes from the end.
After getting halfway to Middlesbrough last week before finding out the game had been postponed due to a frozen pitch, the young side were aiming to extend their unbeaten run in the league to four games.
Jose Angelino’s splendid strike rescued a draw last time out against Newcastle, after two morale-boosting wins against Arsenal and Blackburn.
Norwich provided a tough test for Adam Sadler’s men, having lost just one of their last five league games and advancing to the quarter-finals of the FA Youth Cup.
Ian Lawlor has been representing the EDS since Eirik Johansen’s loan move to Scunthorpe which meant another opportunity for Angus Gunn to impress between the posts.
There were also starts for James Hardy, Ashley Smith-Brown, Jack Byrne and Brandon Barker as Sadler made four changes from the line up that started against Newcastle.
Louis Hutton, Joe Nuttall and Dom McHale dropped to the bench.
City began the brighter of the two teams and enjoyed the best of the first half. Jorge Intima enjoyed another strong performance on the right wing and was at the centre of several Blues chances.
After forcing his way past two Norwich defenders he sent a cross scurrying across the face of goal but no one could quite apply the necessary touch.
Others were also creating promising openings – Barker shot just wide on the half hour and Smith-Brown fired high and wide on his return from injury.
On the stroke of half time City might have had a first penalty after handball in the box but the referee waved for a corner, which forced a good save from the Canaries keeper before smacking back off the bar.
The game became scrappier after the break and there were fewer chances, although the Norwich keeper did stretch his fingertips to tip the ball away from goal after a powerful run down the centre from half time substitute Hutton.
Deadlock was finally broken on the hour mark when Intima tumbled in the area and the referee did point to the spot this time. Horsfield’s confident kick smashed into the back of the net to the keeper’s left to give City the lead.
Norwich’s equaliser fifteen minutes later came from a free kick in a central position just outside the area, and it was a beautiful strike from captain Cameron McGeehan that beat Gunn to sail into the top corner.
City kept chasing a winner at the death, forcing a succession of corners in the five minutes of stoppage time, and Brandon Barker had a good shot deflected just past the post.
But it was not to be and both sides had to settle for the point which preserves City’s unbeaten league run since February 9.
The young Blues are next in action next Saturday at home to Middlesbrough.