Yousef Salech scored a last-minute equaliser as Brian Barry-Murphy's side stole a point against a superior Stockport County at Edgeley Park.
The hosts will rue their missed opportunities and should have been out of sight when Salech's free header earned a point for the Bluebirds.
Stockport striker Benony Breki Andresson had two good chances to take the lead, before referee Simon Mather awarded a penalty for a foul on the Icelandic youngster by Perry Ng.
Norwood sent Cardiff goalkeeper Nathan Trott the wrong way, as the on-loan Copenhagen goalkeeper conceded for the first time since joining the Bluebirds.
Joseph Olowu, Jack Diamond and Andresson all had chances to extend the lead, while Cardiff offered very little in the way of threat at the other end.
That was until the 96th minutes, when Chris Willock's looping cross found an unmarked Salech, who nodded the ball past Corey Addai, with the travelling supporters behind the goal spilling onto the pitch in celebration.
Stockport dropped to 10th in League One after conceding late on, while Cardiff hang onto top spot on goal difference above Bradford City - with a top-two clash at the Cardiff City Stadium on the cards next weekend.
The first real chance of the game came Stockport's way on 25 minutes, when Kyle Wootton's flick-on played through Andresson, whose shot beat Trott but came off the foot of the post and bounced to safety.
The hosts should have been ahead seven minutes later, when Ben Osborne's cross found Andresson between the two Cardiff centre-backs, but his header was straight at Trott, who still had to make an excellent reflex save.
A minute later the hosts were awarded a penalty, as Ng got the wrong side of Andresson and bundled the Stockport striker to the ground.
Up stepped Norwood to score his third goal of the season, as Stockport took a deserved lead.
The lead should have been doubled when Ryan Wintle was dispossessed and Wootton found Andresson inside the Cardiff box, but Will Fish got back to make a crucial deflection.
And the onslaught continued from the resulting corner as Joseph Olowu was left unmarked eight yards out, but he could not keep his volley down and Cardiff escaped again.
The second half started as the first ended, with Stockport committing numbers forward and working their way into the Cardiff box, this time Jack Diamond denied by Trott.
Cardiff thought they had found an equaliser against the run of play when Chris Willock's low cross was poked home by Salech, but the flag had already gone up for offside against Willock.
And as Stockport took their foot off the gas in the seven minutes of added time, Salech's late header stole a point for the league leaders.
Stockport County: Addai, Pye, Olowu, Onyango (O'Keeffe 81'), Osborn, Norwood, Bailey (Camps 73'), Hills, Diamond (Connolly 90'), Andrésson (Moxon 73'), Wootton. Subs Not Used: Hinchliffe, Mothersille, Lowe.
Cardiff City: Trott, Ng (Kpakio 72'), Chambers (Lawlor 72'), Fish, Bagan, Wintle (Robinson 72'), J.Colwill (Turnbull 63'), R.Colwill, Ashford (Davies 63'), Willock, Salech. Subs Not Used: Turner, Osho.
