Norwich's Bradley Johnson and Newcastle's Loic Remy were dismissed with 10 minutes remaining following a clash where the Magpies striker had appeared to aim a head-butt at Johnson after a clash between the pair.
Newcastle dominated the first half, hitting the woodwork twice when a rebound off Johnson struck the left upright while Remy's curling effort beat goalkeeper John Ruddy but hit the other post.
Norwich were clinging on when Hatem Ben Arfa mis-hit a good opportunity into the ground and over the bar, with only a Gary Hooper effort that forced Tim Krul into action their solitary moment of note before the break.
The hosts were kept on the back foot afterwards, with Remy hitting the bar again but Hooper did likewise prior to a lively end to proceedings.
Remy and Johnson's shoving match escalated when the Newcastle striker leaned into the Norwich midfielder with his head. Referee Chris Foy sent the Frenchman off, and after consulting with his assistant Johnson also received his marching orders.
Norwich came close to claiming three points just into stoppage time when Robert Snodgrass's low header was deflected wide by Krul's left leg.
Earlier, Newcastle made a bright start in terrible conditions as the rain lashed down at Carrow Road.
Remy was fouled by Snodgrass on the left side of the penalty area, but Davide Santon's free-kick was straight into the wall.
Norwich finally came to life when a clever turn from Hooper saw the ball fed back to Leroy Fer and the Dutchman's 20-yard drive was deflected behind.
Newcastle almost swept ahead on 18 minutes when full-back Martin Olsson gave the ball away in midfield and Moussa Sissoko darted away down the right channel before cutting a ball back across the six-yard box. Remy arrived on cue, but his snapshot was saved a point-blank range by England goalkeeper Ruddy.
The Norwich goal continued to lead a charmed life as a left-wing cross from Remy was knocked against the base of the post by Canaries midfielder Johnson. A couple of minutes later Remy broke down the left flank before curling a lovely strike goalwards, which struck the outside of the other upright.
Ruddy then had to be alert to beat away a 20-yard effort from Ben Arfa which deflected off Sebastien Bassong and Newcastle cut Norwich apart down the left again just before half-time, but Ben Arfa sent a lovely cross from Sammy Ameobi over the bar.
Finally Krul had something to do as he got down to save a low 20-yard effort from Hooper, which was touched behind before Anthony Pilkington could get to the rebound.
Frustrations boiled over as Scotland winger Snodgrass was involved in a heated exchange with home supporters in the City Stand after another poor corner before Hughton's men were booed off at half-time.
Newcastle were soon back on the offensive and the woodwork saved Norwich again on the hour when Remy whipped a free-kick up over the wall, only to see his effort crash against the crossbar.
Norwich then almost snatched the lead when substitute Nathan Redmond's cross from the left was turned goalwards by Hooper, but Krul was equal to it and pushed the ball up onto the crossbar.
The match turned ugly on 82 minutes when Remy and Johnson exchanged pushes before squaring up head-to-head on the nearside touchline. A melee ensued, before when order was restored the referee correctly showed both men a red card.
Snodgrass could have finished the hero in the final minute but somehow Krul made a crucial save.