Rob Earnshaw's penalty looked like being enough to secure victory for Norwich before Rowlands' left-footed effort denied the Canaries their first away win since April.
It was no more than the outstanding Rowlands deserved after a brilliant performance from the fit-again Republic of Ireland midfielder.
Peter Grant, who watched from the stands and will be confirmed as Norwich manager next week, saw his side make a dream start.
They went ahead after just three minutes when Darren Huckerby latched on to Carl Robinson's through ball and slotted past goalkeeper Paul Jones.
A superb save from Jones prevented Norwich from going further ahead eight minutes later. Earnshaw's header from Lee Croft's right-wing cross was heading for the corner of the net before Jones stretched to tip the ball around the post.
But after a shaky start, Rangers settled and Lee Cook fired wide of the target after jinking his way past City full-back Adam Drury.
Cook then set up the equaliser for Jimmy Smith, laying the ball into the path of the on-loan Chelsea youngster, who drilled home from 20 yards.
Rangers kept the pressure up and Rowlands shot wide after dribbling past Drury, and Dexter Blackstock volleyed just over after Cook's corner was only half-cleared.
Just as Norwich looked likely to get to the interval on level terms, they fell behind on the stroke of half-time.
Jason Shackell was harshly adjudged to have fouled Blackstock and from the resulting free-kick, Marc Bircham touched the ball to Rowlands who fired past the motionless Paul Gallacher.
Rowlands started the second half as he ended the first, giving Drury a torrid time on the right flank.
Straight after the restart Rowlands again turned the Norwich defender inside out and Gallacher had to produce a fine save to keep out his shot.
Rangers' teenage striker Ray Jones saw his header cleared off the line by Jurgen Colin, before Norwich drew level in the 73rd minute.
Croft found space on the right and pulled back for substitute Dion Dublin to net his first Norwich goal.
Worse followed for the R's ten minutes later. Zesh Rehman fouled Huckerby after the Norwich man robbed him near the by-line and a penalty was awarded.
Jones dived the right way but was unable to keep out Earnshaw's spot-kick, and Norwich looked set to inflict Rangers' first defeat since John Gregory took over as manager.
But Rowlands had the final say, letting fly with a half-volley that Gallacher allowed to squirm past him at the near post.